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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 jgs 102 \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}

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