doc/user/finleyelements.tex

%
%           Copyright © 2006 by ACcESS MNRF
%               \url{http://www.access.edu.au
%         Primary Business: Queensland, Australia.
%   Licensed under the Open Software License version 3.0
%      http://www.opensource.org/licenses/osl-3.0.php
%
\setlength{\unitlength}{1mm}

\newsavebox{\HLa}
\savebox{\HLa}(0,0)
  {\put(0,0){\circle*{2}}
   \thicklines \put(1,0){\line(1,0){28}}
   \put(30,0){\circle*{2}} }

\newsavebox{\HLathin}
\savebox{\HLathin}(0,0)
  {\put(0,0){\circle{2}}
   \thinlines \put(1,0){\line(1,0){28}}
   \put(30,0){\circle{2}} }

\newsavebox{\VLa}
\savebox{\VLa}(0,30)
  {\put(0,0){\circle*{2}}
   \thicklines \put(0,1){\line(0,1){28}}
   \put(0,30){\circle*{2}} }

\newsavebox{\VLathin}
\savebox{\VLathin}(0,30)
  {\put(0,0){\circle{2}}
   \thinlines \put(0,1){\line(0,1){28}}
   \put(0,30){\circle{2}} }

\newsavebox{\SLax}
\savebox{\SLax}(0,30)
  {\thicklines \put(0,0){\line(-1,1){30}}
   \put(0,0){\circle*{2}}
   \put(-30,30){\circle*{2}} }

\newsavebox{\SLaa}
\savebox{\SLaa}(0,15)
  {\thicklines \put(0,0){\line(-4,3){20}}
   \put(0,0){\circle*{2}}
   \put(-20,15){\circle*{2}} }

\newsavebox{\SLab}
\savebox{\SLab}(0,-15)
  {\thicklines \put(0,0){\line(-4,-3){20}}
   \put(0,0){\circle*{2}}
   \put(-20,-15){\circle*{2}} }

\newsavebox{\SLabthin}
\savebox{\SLabthin}(0,-15)
  {\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
   \put(0,0){\circle{2}}
   \put(-20,-15){\circle{2}} }

\newsavebox{\SLac}
\savebox{\SLac}(0,15)
  {\thicklines \put(0,0){\line(-2,3){10}}
   \put(0,0){\circle*{2}}
   \put(-10,15){\circle*{2}} }

\newsavebox{\SLacthin}
\savebox{\SLacthin}(0,15)
  {\thinlines \put(0,0){\line(-2,3){9.4}}
   \put(0,0){\circle{2}}
   \put(-10,15){\circle{2}} }


\newsavebox{\HLd}
\savebox{\HLd}(0,0)
  {\put(0,0){\circle*{2}}
   \put(10,0){\circle*{2}}
   \thicklines \put(1,0){\line(1,0){28}}
   \put(20,0){\circle*{2}}
   \put(30,0){\circle*{2}} }

\newsavebox{\HLdthin}
\savebox{\HLdthin}(0,0)
  {\put(0,0){\circle{2}}
   \put(10,0){\circle{2}}
   \thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
   \put(20,0){\circle{2}}
   \put(30,0){\circle{2}} }

\newsavebox{\VLd}
\savebox{\VLd}(0,30)
  {\put(0,0){\circle*{2}}
   \put(0,10){\circle*{2}}
   \thicklines \put(0,1){\line(0,1){28}}
   \put(0,20){\circle*{2}}
   \put(0,30){\circle*{2}} }

\newsavebox{\VLdthin}
\savebox{\VLdthin}(0,30)
  {\put(0,0){\circle{2}}
   \put(0,10){\circle{2}}
   \thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
   \put(0,20){\circle{2}}
   \put(0,30){\circle{2}} }

\newsavebox{\SLf}
\savebox{\SLf}(0,30)
  {\thicklines \put(0,0){\line(-1,1){30}}
   \put(0,0){\circle*{2}}
   \put(-10,10){\circle*{2}}
   \put(-20,20){\circle*{2}}
   \put(-30,30){\circle*{2}} }

\newsavebox{\SLad}
\savebox{\SLad}(0,15)
  {\thicklines \put(0,0){\line(-4,3){20}}
   \put(0,0){\circle*{2}}
   \put(-6.66,5){\circle*{2}}
   \put(-13.33,10){\circle*{2}}
   \put(-20,15){\circle*{2}} }

\newsavebox{\SLbd}
\savebox{\SLbd}(0,-15)
  {\thicklines \put(0,0){\line(-4,-3){20}}
   \put(0,0){\circle*{2}}
   \put(-6.66,-5){\circle*{2}}
   \put(-13.33,-10){\circle*{2}}
   \put(-20,-15){\circle*{2}} }

\newsavebox{\SLbdthin}
\savebox{\SLbdthin}(0,-15)
  {\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
   \put(0,0){\circle{2}}
   \put(-6.66,-5){\circle{2}}
   \put(-13.33,-10){\circle{2}}
   \put(-20,-15){\circle{2}} }

\newsavebox{\SLcd}
\savebox{\SLcd}(0,15)
  {\thicklines \put(0,0){\line(-2,3){10}}
   \put(0,0){\circle*{2}}
   \put(-3.33,5){\circle*{2}}
   \put(-6.66,10){\circle*{2}}
   \put(-10,15){\circle*{2}} }

\newsavebox{\SLcdthin}
\savebox{\SLcdthin}(0,15)
  {\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
   \put(0,0){\circle{2}}
   \put(-3.33,5){\circle{2}}
   \put(-6.66,10){\circle{2}}
   \put(-10,15){\circle{2}} }

\newsavebox{\HLe}
\savebox{\HLe}(0,0)
  {\put(0,0){\circle*{2}}
   \put(15,0){\circle*{2}}
   \thicklines \put(1,0){\line(1,0){28}}
   \put(30,0){\circle*{2}} }

\newsavebox{\HLethin}
\savebox{\HLethin}(0,0)
  {\put(0,0){\circle{2}}
   \put(15,0){\circle{2}}
   \thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
   \put(30,0){\circle{2}} }

\newsavebox{\VLe}
\savebox{\VLe}(0,30)
  {\put(0,0){\circle*{2}}
   \put(0,15){\circle*{2}}
   \thicklines \put(0,1){\line(0,1){28}}
   \put(0,30){\circle*{2}} }

\newsavebox{\VLethin}
\savebox{\VLethin}(0,30)
  {\put(0,0){\circle{2}}
   \put(0,15){\circle{2}}
   \thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
   \put(0,30){\circle{2}} }

\newsavebox{\SLe}
\savebox{\SLe}(0,30)
  {\thicklines \put(0,0){\line(-1,1){30}}
   \put(0,0){\circle*{2}}
   \put(-15,15){\circle*{2}}
   \put(-30,30){\circle*{2}} }

\newsavebox{\SLae}
\savebox{\SLae}(0,15)
  {\thicklines \put(0,0){\line(-4,3){20}}
   \put(0,0){\circle*{2}}
   \put(-10,7.5){\circle*{2}}
   \put(-20,15){\circle*{2}} }

\newsavebox{\SLbe}
\savebox{\SLbe}(0,-15)
  {\thicklines \put(0,0){\line(-4,-3){20}}
   \put(0,0){\circle*{2}}
   \put(-10,-7.5){\circle*{2}}
   \put(-20,-15){\circle*{2}} }

\newsavebox{\SLbethin}
\savebox{\SLbethin}(0,-15)
  {\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
   \put(0,0){\circle{2}}
   \put(-10,-7.5){\circle{2}}
   \put(-20,-15){\circle{2}} }

\newsavebox{\SLce}
\savebox{\SLce}(0,15)
  {\thicklines \put(0,0){\line(-2,3){10}}
   \put(0,0){\circle*{2}}
   \put(-5,7.5){\circle*{2}}
   \put(-10,15){\circle*{2}} }

\newsavebox{\SLcethin}
\savebox{\SLcethin}(0,15)
  {\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
   \put(0,0){\circle{2}}
   \put(-5,7.5){\circle{2}}
   \put(-10,15){\circle{2}} }

%=====================================================================
%
%   order 1
%   -------
%

\begin{figure}


\begin{picture}(170,210) \thicklines


\put(20,205){\circle*{2}}
\put(10,195){\parbox[t]{45mm}
             \finleyelement{Point1}}

\put(90,205){\usebox{\HLa}}
\put(90,195){\parbox[t]{45mm}
             \finleyelement{LINE2} }

\put(10,145){\usebox{\HLa}}
\put(40,145){\usebox{\SLax}}
\put(10,145){\usebox{\VLa}}
\put(10,135){\parbox[t]{45mm}
             \finleyelement{Tri3} }

\put(90,145){\usebox{\HLa}}
\put(90,175){\usebox{\HLa}}
\put(90,145){\usebox{\VLa}}
\put(120,145){\usebox{\VLa}}
\put(90,135){\parbox[t]{45mm}
             \finleyelement{Rec4} }

\put(50,90){\usebox{\HLa}}
\put(80,90){\usebox{\SLax}}
\put(50,90){\usebox{\VLa}}
\put(80,90){\usebox{\SLac}}
\put(70,105){\usebox{\SLabthin}}
\put(70,105){\usebox{\SLaa}}
\put(50,80 ){\parbox[t]{45mm}
             \finleyelement{Tet4} }

\put(90,20){\usebox{\HLa}}
\put(90,50){\usebox{\HLa}}
\put(90,20){\usebox{\VLa}}
\put(120,20){\usebox{\VLa}}
\put(110,35){\usebox{\SLabthin}}
\put(140,35){\usebox{\SLab}}
\put(110,65){\usebox{\SLab}}
\put(140,65){\usebox{\SLab}}
\put(110,35){\usebox{\HLathin}}
\put(110,65){\usebox{\HLa}}
\put(110,35){\usebox{\VLathin}}
\put(140,35){\usebox{\VLa}}
\put(90,10 ){\parbox[t]{45mm}
             \finleyelement{Hex8} }

% nummerierung der punkte:
\put(19,208){{\it 1}} % Point
\put(89,208){{\it 1}} % line
\put(119,208){{\it 2}}
\put(6,174){{\it 3}} % Triangle
\put(6,144){{\it 1}}
\put(43,144){{\it 2}}
\put(86,174){{\it 4}} % quadrilateral
\put(86,144){{\it 1}}
\put(123,174){{\it 3}}
\put(123,144){{\it 2}}
\put(46,119){{\it 4}} % Tetrahedron
\put(46,89){{\it 1}}
\put(83,89){{\it 2}}
\put(73,104){{\it 3}}
\put(86,49){{\it 5}} % Hexahedron
\put(86,19){{\it 1}}
\put(123,49){{\it 6}}
\put(123,19){{\it 2}}
\put(106,64){{\it 8}}
\put(106,34){{\it 4}}
\put(143,64){{\it 7}}
\put(143,34){{\it 3}}

\end{picture}
\caption{\label{FINLEY.FIG:1} Elements of order 1}
\end{figure}
%=====================================================================
%
%
%   order 2
%   -------
%   (boxes in 'fesubelm')


\begin{figure}
\setlength{\unitlength}{1mm}


\begin{picture}(170,210) \thicklines

\put(20,205){\circle*{2}}
\put(10,195){\parbox[t]{45mm}
             \finleyelement{Point1} }

\put(90,205){\usebox{\HLe}}
\put(90,195){\parbox[t]{45mm}
             \finleyelement{LINE3} }

\put(10,145){\usebox{\HLe}}
\put(40,145){\usebox{\SLe}}
\put(10,145){\usebox{\VLe}}
\put(10,135){\parbox[t]{45mm}
             \finleyelement{Tri6} }

\put(90,145){\usebox{\HLe}}
\put(90,175){\usebox{\HLe}}
\put(90,145){\usebox{\VLe}}
\put(120,145){\usebox{\VLe}}
\put(90,135){\parbox[t]{45mm}
             \finleyelement{Rec8} }

\put(50,90){\usebox{\HLe}}
\put(80,90){\usebox{\SLe}}
\put(50,90){\usebox{\VLe}}
\put(80,90){\usebox{\SLce}}
\put(70,105){\usebox{\SLbethin}}
\put(70,105){\usebox{\SLae}}
\put(50,80 ){\parbox[t]{45mm}
             \finleyelement{Tet10} }

\put(90,20){\usebox{\HLe}}
\put(90,50){\usebox{\HLe}}
\put(90,20){\usebox{\VLe}}
\put(120,20){\usebox{\VLe}}
\put(110,35){\usebox{\SLbethin}}
\put(140,35){\usebox{\SLbe}}
\put(110,65){\usebox{\SLbe}}
\put(140,65){\usebox{\SLbe}}
\put(110,35){\usebox{\HLethin}}
\put(110,65){\usebox{\HLe}}
\put(110,35){\usebox{\VLethin}}
\put(140,35){\usebox{\VLe}}
\put(90,10 ){\parbox[t]{45mm}
             \finleyelement{Hex20} }


% nummerierung der punkte:
\put(19,208){{\it 1}} % Point
\put(89,208){{\it 1}} % line
\put(104,208){{\it 3}}
\put(119,208){{\it 2}}
\put(6,174){{\it 3}} % Triangle
\put(6,159){{\it 6}}
\put(6,144){{\it 1}}
\put(28,159){{\it 5}}
\put(43,144){{\it 2}}
\put(24,140){{\it 4}}
\put(104,140){{\it 5}} % quaTrilateral
\put(86,174){{\it 4}}
\put(86,159){{\it 8}}
\put(86,144){{\it 1}}
\put(104,178){{\it 7}}
\put(123,174){{\it 3}}
\put(123,159){{\it 6}}
\put(123,144){{\it 2}}
\put(64,85){{\it 5}} % Tetrahedron
\put(46,119){{\it 4}}
\put(46,104){{\it 8}}
\put(46,89){{\it 1}}
\put(61,104){{\it 9}}
\put(83,89){{\it 2}}
\put(56,96.5){{\it 7}}
\put(78,96.5){{\it 6}}
\put(73,104){{\it 3}}
\put(62.5,111.5){{\it 10}}
\put(104,15){{\it 9}} % Hexahedron
\put(86,49){{\it 5}}
\put(85,34){{\it 13}}
\put(86,19){{\it 1}}
\put(104,52){{\it 17}}
\put(123,49){{\it 6}}
\put(115,37){{\it 14}}
\put(123,19){{\it 2}}
\put(125,37){{\it 11}}
\put(106,64){{\it 8}}
\put(112,46){{\it 16}}
\put(106,34){{\it 4}}
\put(124,68){{\it 19}}
\put(143,64){{\it 7}}
\put(142,49){{\it 15}}
\put(143,34){{\it 3}}
\put(94.5,26.5){{\it 12}}
\put(132.5,26.5){{\it 10}}
\put(94.5,56.5){{\it 20}}
\put(132.5,56.5){{\it 18}}

\end{picture}
\caption{\label{FINLEY.FIG:2} Elements of order 2}
\end{figure}

%
% additional elements
%
\begin{figure}
\begin{picture}(170,210) \thicklines

\put(50,095){\usebox{\HLe}}
\put(50,125){\usebox{\HLe}}
\put(50,095){\usebox{\VLe}}
\put(80,095){\usebox{\VLe}}
\put(65,110){\circle*{2}}
\put(50,085){\parbox[t]{45mm}
             \finleyelement{Rec9} }


\put(64,090){{\it 5}}
\put(46,124){{\it 4}}
\put(46,109){{\it 8}}
\put(46,094){{\it 1}}
\put(64,128){{\it 7}}
\put(83,124){{\it 3}}
\put(83,109){{\it 6}}
\put(83,094){{\it 2}}
\put(64,105){{\it 9}}


\end{picture}
\caption{\label{FINLEY.FIG:4} Additional shape functions}
\end{figure}
1	%
2	% Copyright © 2006 by ACcESS MNRF
3	% \url{http://www.access.edu.au
4	% Primary Business: Queensland, Australia.
5	% Licensed under the Open Software License version 3.0
6	% http://www.opensource.org/licenses/osl-3.0.php
7	%
8	\setlength{\unitlength}{1mm}
9
10	\newsavebox{\HLa}
11	\savebox{\HLa}(0,0)
12	{\put(0,0){\circle*{2}}
13	\thicklines \put(1,0){\line(1,0){28}}
14	\put(30,0){\circle*{2}} }
15
16	\newsavebox{\HLathin}
17	\savebox{\HLathin}(0,0)
18	{\put(0,0){\circle{2}}
19	\thinlines \put(1,0){\line(1,0){28}}
20	\put(30,0){\circle{2}} }
21
22	\newsavebox{\VLa}
23	\savebox{\VLa}(0,30)
24	{\put(0,0){\circle*{2}}
25	\thicklines \put(0,1){\line(0,1){28}}
26	\put(0,30){\circle*{2}} }
27
28	\newsavebox{\VLathin}
29	\savebox{\VLathin}(0,30)
30	{\put(0,0){\circle{2}}
31	\thinlines \put(0,1){\line(0,1){28}}
32	\put(0,30){\circle{2}} }
33
34	\newsavebox{\SLax}
35	\savebox{\SLax}(0,30)
36	{\thicklines \put(0,0){\line(-1,1){30}}
37	\put(0,0){\circle*{2}}
38	\put(-30,30){\circle*{2}} }
39
40	\newsavebox{\SLaa}
41	\savebox{\SLaa}(0,15)
42	{\thicklines \put(0,0){\line(-4,3){20}}
43	\put(0,0){\circle*{2}}
44	\put(-20,15){\circle*{2}} }
45
46	\newsavebox{\SLab}
47	\savebox{\SLab}(0,-15)
48	{\thicklines \put(0,0){\line(-4,-3){20}}
49	\put(0,0){\circle*{2}}
50	\put(-20,-15){\circle*{2}} }
51
52	\newsavebox{\SLabthin}
53	\savebox{\SLabthin}(0,-15)
54	{\thinlines \put(-0.7,-0.7){\line(-4,-3){18.7}}
55	\put(0,0){\circle{2}}
56	\put(-20,-15){\circle{2}} }
57
58	\newsavebox{\SLac}
59	\savebox{\SLac}(0,15)
60	{\thicklines \put(0,0){\line(-2,3){10}}
61	\put(0,0){\circle*{2}}
62	\put(-10,15){\circle*{2}} }
63
64	\newsavebox{\SLacthin}
65	\savebox{\SLacthin}(0,15)
66	{\thinlines \put(0,0){\line(-2,3){9.4}}
67	\put(0,0){\circle{2}}
68	\put(-10,15){\circle{2}} }
69
70
71	\newsavebox{\HLd}
72	\savebox{\HLd}(0,0)
73	{\put(0,0){\circle*{2}}
74	\put(10,0){\circle*{2}}
75	\thicklines \put(1,0){\line(1,0){28}}
76	\put(20,0){\circle*{2}}
77	\put(30,0){\circle*{2}} }
78
79	\newsavebox{\HLdthin}
80	\savebox{\HLdthin}(0,0)
81	{\put(0,0){\circle{2}}
82	\put(10,0){\circle{2}}
83	\thinlines \multiput(1,0)(10,0){3}{\line(1,0){8}}
84	\put(20,0){\circle{2}}
85	\put(30,0){\circle{2}} }
86
87	\newsavebox{\VLd}
88	\savebox{\VLd}(0,30)
89	{\put(0,0){\circle*{2}}
90	\put(0,10){\circle*{2}}
91	\thicklines \put(0,1){\line(0,1){28}}
92	\put(0,20){\circle*{2}}
93	\put(0,30){\circle*{2}} }
94
95	\newsavebox{\VLdthin}
96	\savebox{\VLdthin}(0,30)
97	{\put(0,0){\circle{2}}
98	\put(0,10){\circle{2}}
99	\thinlines \multiput(0,1)(0,10){3}{\line(0,1){8}}
100	\put(0,20){\circle{2}}
101	\put(0,30){\circle{2}} }
102
103	\newsavebox{\SLf}
104	\savebox{\SLf}(0,30)
105	{\thicklines \put(0,0){\line(-1,1){30}}
106	\put(0,0){\circle*{2}}
107	\put(-10,10){\circle*{2}}
108	\put(-20,20){\circle*{2}}
109	\put(-30,30){\circle*{2}} }
110
111	\newsavebox{\SLad}
112	\savebox{\SLad}(0,15)
113	{\thicklines \put(0,0){\line(-4,3){20}}
114	\put(0,0){\circle*{2}}
115	\put(-6.66,5){\circle*{2}}
116	\put(-13.33,10){\circle*{2}}
117	\put(-20,15){\circle*{2}} }
118
119	\newsavebox{\SLbd}
120	\savebox{\SLbd}(0,-15)
121	{\thicklines \put(0,0){\line(-4,-3){20}}
122	\put(0,0){\circle*{2}}
123	\put(-6.66,-5){\circle*{2}}
124	\put(-13.33,-10){\circle*{2}}
125	\put(-20,-15){\circle*{2}} }
126
127	\newsavebox{\SLbdthin}
128	\savebox{\SLbdthin}(0,-15)
129	{\thinlines \multiput(-0.7,-0.7)(-6.66,-5){3}{\line(-4,-3){5.1}}
130	\put(0,0){\circle{2}}
131	\put(-6.66,-5){\circle{2}}
132	\put(-13.33,-10){\circle{2}}
133	\put(-20,-15){\circle{2}} }
134
135	\newsavebox{\SLcd}
136	\savebox{\SLcd}(0,15)
137	{\thicklines \put(0,0){\line(-2,3){10}}
138	\put(0,0){\circle*{2}}
139	\put(-3.33,5){\circle*{2}}
140	\put(-6.66,10){\circle*{2}}
141	\put(-10,15){\circle*{2}} }
142
143	\newsavebox{\SLcdthin}
144	\savebox{\SLcdthin}(0,15)
145	{\thinlines \multiput(-0.6,0.8)(-3.33,5){3}{\line(-2,3){2.35}}
146	\put(0,0){\circle{2}}
147	\put(-3.33,5){\circle{2}}
148	\put(-6.66,10){\circle{2}}
149	\put(-10,15){\circle{2}} }
150
151	\newsavebox{\HLe}
152	\savebox{\HLe}(0,0)
153	{\put(0,0){\circle*{2}}
154	\put(15,0){\circle*{2}}
155	\thicklines \put(1,0){\line(1,0){28}}
156	\put(30,0){\circle*{2}} }
157
158	\newsavebox{\HLethin}
159	\savebox{\HLethin}(0,0)
160	{\put(0,0){\circle{2}}
161	\put(15,0){\circle{2}}
162	\thinlines \multiput(1,0)(15,0){2}{\line(1,0){13}}
163	\put(30,0){\circle{2}} }
164
165	\newsavebox{\VLe}
166	\savebox{\VLe}(0,30)
167	{\put(0,0){\circle*{2}}
168	\put(0,15){\circle*{2}}
169	\thicklines \put(0,1){\line(0,1){28}}
170	\put(0,30){\circle*{2}} }
171
172	\newsavebox{\VLethin}
173	\savebox{\VLethin}(0,30)
174	{\put(0,0){\circle{2}}
175	\put(0,15){\circle{2}}
176	\thinlines \multiput(0,1)(0,15){2}{\line(0,1){13}}
177	\put(0,30){\circle{2}} }
178
179	\newsavebox{\SLe}
180	\savebox{\SLe}(0,30)
181	{\thicklines \put(0,0){\line(-1,1){30}}
182	\put(0,0){\circle*{2}}
183	\put(-15,15){\circle*{2}}
184	\put(-30,30){\circle*{2}} }
185
186	\newsavebox{\SLae}
187	\savebox{\SLae}(0,15)
188	{\thicklines \put(0,0){\line(-4,3){20}}
189	\put(0,0){\circle*{2}}
190	\put(-10,7.5){\circle*{2}}
191	\put(-20,15){\circle*{2}} }
192
193	\newsavebox{\SLbe}
194	\savebox{\SLbe}(0,-15)
195	{\thicklines \put(0,0){\line(-4,-3){20}}
196	\put(0,0){\circle*{2}}
197	\put(-10,-7.5){\circle*{2}}
198	\put(-20,-15){\circle*{2}} }
199
200	\newsavebox{\SLbethin}
201	\savebox{\SLbethin}(0,-15)
202	{\thinlines \multiput(-0.7,-0.7)(-10,-7.5){2}{\line(-4,-3){8.4}}
203	\put(0,0){\circle{2}}
204	\put(-10,-7.5){\circle{2}}
205	\put(-20,-15){\circle{2}} }
206
207	\newsavebox{\SLce}
208	\savebox{\SLce}(0,15)
209	{\thicklines \put(0,0){\line(-2,3){10}}
210	\put(0,0){\circle*{2}}
211	\put(-5,7.5){\circle*{2}}
212	\put(-10,15){\circle*{2}} }
213
214	\newsavebox{\SLcethin}
215	\savebox{\SLcethin}(0,15)
216	{\thinlines \multiput(-0.6,0.8)(-5,7.5){2}{\line(-2,3){3.9}}
217	\put(0,0){\circle{2}}
218	\put(-5,7.5){\circle{2}}
219	\put(-10,15){\circle{2}} }
220
221	%=====================================================================
222	%
223	% order 1
224	% -------
225	%
226
227	\begin{figure}
228
229
230	\begin{picture}(170,210) \thicklines
231
232
233
234	\put(20,205){\circle*{2}}
235	\put(10,195){\parbox[t]{45mm}
236	\finleyelement{Point1}}
237
238	\put(90,205){\usebox{\HLa}}
239	\put(90,195){\parbox[t]{45mm}
240	\finleyelement{LINE2} }
241
242	\put(10,145){\usebox{\HLa}}
243	\put(40,145){\usebox{\SLax}}
244	\put(10,145){\usebox{\VLa}}
245	\put(10,135){\parbox[t]{45mm}
246	\finleyelement{Tri3} }
247
248	\put(90,145){\usebox{\HLa}}
249	\put(90,175){\usebox{\HLa}}
250	\put(90,145){\usebox{\VLa}}
251	\put(120,145){\usebox{\VLa}}
252	\put(90,135){\parbox[t]{45mm}
253	\finleyelement{Rec4} }
254
255	\put(50,90){\usebox{\HLa}}
256	\put(80,90){\usebox{\SLax}}
257	\put(50,90){\usebox{\VLa}}
258	\put(80,90){\usebox{\SLac}}
259	\put(70,105){\usebox{\SLabthin}}
260	\put(70,105){\usebox{\SLaa}}
261	\put(50,80 ){\parbox[t]{45mm}
262	\finleyelement{Tet4} }
263
264	\put(90,20){\usebox{\HLa}}
265	\put(90,50){\usebox{\HLa}}
266	\put(90,20){\usebox{\VLa}}
267	\put(120,20){\usebox{\VLa}}
268	\put(110,35){\usebox{\SLabthin}}
269	\put(140,35){\usebox{\SLab}}
270	\put(110,65){\usebox{\SLab}}
271	\put(140,65){\usebox{\SLab}}
272	\put(110,35){\usebox{\HLathin}}
273	\put(110,65){\usebox{\HLa}}
274	\put(110,35){\usebox{\VLathin}}
275	\put(140,35){\usebox{\VLa}}
276	\put(90,10 ){\parbox[t]{45mm}
277	\finleyelement{Hex8} }
278
279	% nummerierung der punkte:
280	\put(19,208){{\it 1}} % Point
281	\put(89,208){{\it 1}} % line
282	\put(119,208){{\it 2}}
283	\put(6,174){{\it 3}} % Triangle
284	\put(6,144){{\it 1}}
285	\put(43,144){{\it 2}}
286	\put(86,174){{\it 4}} % quadrilateral
287	\put(86,144){{\it 1}}
288	\put(123,174){{\it 3}}
289	\put(123,144){{\it 2}}
290	\put(46,119){{\it 4}} % Tetrahedron
291	\put(46,89){{\it 1}}
292	\put(83,89){{\it 2}}
293	\put(73,104){{\it 3}}
294	\put(86,49){{\it 5}} % Hexahedron
295	\put(86,19){{\it 1}}
296	\put(123,49){{\it 6}}
297	\put(123,19){{\it 2}}
298	\put(106,64){{\it 8}}
299	\put(106,34){{\it 4}}
300	\put(143,64){{\it 7}}
301	\put(143,34){{\it 3}}
302
303	\end{picture}
304	\caption{\label{FINLEY.FIG:1} Elements of order 1}
305	\end{figure}
306	%=====================================================================
307	%
308	%
309	% order 2
310	% -------
311	% (boxes in 'fesubelm')
312
313
314	\begin{figure}
315	\setlength{\unitlength}{1mm}
316
317
318
319	\begin{picture}(170,210) \thicklines
320
321	\put(20,205){\circle*{2}}
322	\put(10,195){\parbox[t]{45mm}
323	\finleyelement{Point1} }
324
325	\put(90,205){\usebox{\HLe}}
326	\put(90,195){\parbox[t]{45mm}
327	\finleyelement{LINE3} }
328
329	\put(10,145){\usebox{\HLe}}
330	\put(40,145){\usebox{\SLe}}
331	\put(10,145){\usebox{\VLe}}
332	\put(10,135){\parbox[t]{45mm}
333	\finleyelement{Tri6} }
334
335	\put(90,145){\usebox{\HLe}}
336	\put(90,175){\usebox{\HLe}}
337	\put(90,145){\usebox{\VLe}}
338	\put(120,145){\usebox{\VLe}}
339	\put(90,135){\parbox[t]{45mm}
340	\finleyelement{Rec8} }
341
342	\put(50,90){\usebox{\HLe}}
343	\put(80,90){\usebox{\SLe}}
344	\put(50,90){\usebox{\VLe}}
345	\put(80,90){\usebox{\SLce}}
346	\put(70,105){\usebox{\SLbethin}}
347	\put(70,105){\usebox{\SLae}}
348	\put(50,80 ){\parbox[t]{45mm}
349	\finleyelement{Tet10} }
350
351	\put(90,20){\usebox{\HLe}}
352	\put(90,50){\usebox{\HLe}}
353	\put(90,20){\usebox{\VLe}}
354	\put(120,20){\usebox{\VLe}}
355	\put(110,35){\usebox{\SLbethin}}
356	\put(140,35){\usebox{\SLbe}}
357	\put(110,65){\usebox{\SLbe}}
358	\put(140,65){\usebox{\SLbe}}
359	\put(110,35){\usebox{\HLethin}}
360	\put(110,65){\usebox{\HLe}}
361	\put(110,35){\usebox{\VLethin}}
362	\put(140,35){\usebox{\VLe}}
363	\put(90,10 ){\parbox[t]{45mm}
364	\finleyelement{Hex20} }
365
366
367	% nummerierung der punkte:
368	\put(19,208){{\it 1}} % Point
369	\put(89,208){{\it 1}} % line
370	\put(104,208){{\it 3}}
371	\put(119,208){{\it 2}}
372	\put(6,174){{\it 3}} % Triangle
373	\put(6,159){{\it 6}}
374	\put(6,144){{\it 1}}
375	\put(28,159){{\it 5}}
376	\put(43,144){{\it 2}}
377	\put(24,140){{\it 4}}
378	\put(104,140){{\it 5}} % quaTrilateral
379	\put(86,174){{\it 4}}
380	\put(86,159){{\it 8}}
381	\put(86,144){{\it 1}}
382	\put(104,178){{\it 7}}
383	\put(123,174){{\it 3}}
384	\put(123,159){{\it 6}}
385	\put(123,144){{\it 2}}
386	\put(64,85){{\it 5}} % Tetrahedron
387	\put(46,119){{\it 4}}
388	\put(46,104){{\it 8}}
389	\put(46,89){{\it 1}}
390	\put(61,104){{\it 9}}
391	\put(83,89){{\it 2}}
392	\put(56,96.5){{\it 7}}
393	\put(78,96.5){{\it 6}}
394	\put(73,104){{\it 3}}
395	\put(62.5,111.5){{\it 10}}
396	\put(104,15){{\it 9}} % Hexahedron
397	\put(86,49){{\it 5}}
398	\put(85,34){{\it 13}}
399	\put(86,19){{\it 1}}
400	\put(104,52){{\it 17}}
401	\put(123,49){{\it 6}}
402	\put(115,37){{\it 14}}
403	\put(123,19){{\it 2}}
404	\put(125,37){{\it 11}}
405	\put(106,64){{\it 8}}
406	\put(112,46){{\it 16}}
407	\put(106,34){{\it 4}}
408	\put(124,68){{\it 19}}
409	\put(143,64){{\it 7}}
410	\put(142,49){{\it 15}}
411	\put(143,34){{\it 3}}
412	\put(94.5,26.5){{\it 12}}
413	\put(132.5,26.5){{\it 10}}
414	\put(94.5,56.5){{\it 20}}
415	\put(132.5,56.5){{\it 18}}
416
417	\end{picture}
418	\caption{\label{FINLEY.FIG:2} Elements of order 2}
419	\end{figure}
420
421	%
422	% additional elements
423	%
424	\begin{figure}
425	\begin{picture}(170,210) \thicklines
426
427	\put(50,095){\usebox{\HLe}}
428	\put(50,125){\usebox{\HLe}}
429	\put(50,095){\usebox{\VLe}}
430	\put(80,095){\usebox{\VLe}}
431	\put(65,110){\circle*{2}}
432	\put(50,085){\parbox[t]{45mm}
433	\finleyelement{Rec9} }
434
435
436	\put(64,090){{\it 5}}
437	\put(46,124){{\it 4}}
438	\put(46,109){{\it 8}}
439	\put(46,094){{\it 1}}
440	\put(64,128){{\it 7}}
441	\put(83,124){{\it 3}}
442	\put(83,109){{\it 6}}
443	\put(83,094){{\it 2}}
444	\put(64,105){{\it 9}}
445
446
447	\end{picture}
448	\caption{\label{FINLEY.FIG:4} Additional shape functions}
449	\end{figure}
Name	Value
svn:eol-style	native
svn:keywords	Author Date Id Revision