Patch test

Patch test for arbitrary three node triangle element

Element	Nodes
1	1	2	5
2	5	2	6
3	6	2	7
4	5	6	7
5	1	5	8
6	5	7	8
7	1	8	4
8	4	8	7
9	2	3	7
10	4	7	3

Node	Coordinates		Boundary conditions		Solution
	X	Y	u	v	u	v
1	0	0	0	0	0	0
2	2	0	0.002	0.001	0.002	0.001
3	2	3	0.0035	0.004	0.0035	0.004
4	0	2	0.001	0.002	0.001	0.002
5	0.4	0.4	-	-	0.0006	0.0006
6	1.4	0.6	-	-	0.0017	0.0013
7	1.5	2.	-	-	0.0025	0.00275
8	0.3	1.6	-	-	0.0011	0.00175

Patch test for arbitrary four node quadrilateral element

Element	Nodes
1	1	2	6	5
2	1	5	8	4
3	5	6	7	8
4	6	2	3	7
5	8	7	3	4

Node	Coordinates		Boundary conditions		Solution
	X	Y	u	v	u	v
1	0	0	0	0	0	0
2	2	0	0.002	0.001	0.002	0.001
3	2	3	0.0035	0.004	0.0035	0.004
4	0	2	0.001	0.002	0.001	0.002
5	0.4	0.4	-	-	0.0006	0.0006
6	1.4	0.6	-	-	0.0017	0.0013
7	1.5	2.	-	-	0.0025	0.00275
8	0.3	1.6	-	-	0.0011	0.00175

Patch test for arbitrary six node triangle element

Element	Nodes
1	1	2	5	9	10	11
2	5	2	6	10	12	13
3	6	2	7	12	14	15
4	5	6	7	13	15	16
5	1	5	8	11	17	18
6	5	7	8	16	19	17
7	1	8	4	18	20	21
8	4	8	7	20	19	22
9	2	3	7	23	24	14
10	4	7	3	22	24	25

Node	Coordinates		Boundary conditions		Solution
	X	Y	u	v	u	v
1	0.05	0	0.00005	0.000025	0.00005	0.000025
2	2	0	0.002	0.001	0.002	0.001
3	2.05	3	0.00355	0.004025	0.00355	0.004025
4	0	2.05	0.001025	0.00205	0.001025	0.00205
5	0.45	0.4	-	-	0.00065	0.000625
6	1.4	0.6	-	-	0.0017	0.0013
7	1.5	2.	-	-	0.0025	0.00275
8	0.3	1.6	-	-	0.0011	0.00175
9	1.	0.05	0.001025	0.00055	0.001025	0.00055
10	1.25	0.25	-	-	0.001375	0.000875
11	0.25	0.25	-	-	0.000375	0.000375
12	1.75	0.35	-	-	0.001925	0.001225
13	0.9	0.5	-	-	0.00115	0.00095
14	1.8	1.	-	-	0.0023	0.0019
15	1.5	1.35	-	-	0.002175	0.0021
16	0.95	1.2	-	-	0.00155	0.001675
17	0.4	1.	-	-	0.0009	0.0012
18	0.2	0.85	-	-	0.000625	0.00095
19	0.95	1.8	-	-	0.00185	0.002275
20	0.2	1.8	-	-	0.0011	0.0019
21	0.05	1.	0.00055	0.001025	0.00055	0.001025
22	0.75	2.	-	-	0.00175	0.002375
23	2.05	1.5	0.0028	0.002525	0.0028	0.002525
24	1.75	2.5	-	-	0.003	0.003375
25	1.05	2.5	0.0023	0.003025	0.0023	0.003025

Patch test for arbitrary three dimensional four node element

Element	Nodes
1	12	9	13	1
2	8	13	5	1
3	12	1	8	4
4	12	13	8	1
5	12	13	16	8
6	1	9	13	10
7	6	13	14	10
8	1	10	6	2
9	1	13	6	10
10	1	13	5	6
11	3	2	6	10
12	15	6	14	10
13	3	10	15	11
14	3	6	15	10
15	3	6	7	15
16	3	11	15	12
17	8	15	16	12
18	3	12	8	4
19	3	15	8	12
20	3	15	7	8
21	8	5	13	6
22	15	13	14	6
23	8	6	15	7
24	8	13	15	6
25	8	13	16	15
26	12	9	1	10
27	3	1	2	10
28	12	10	3	11
29	12	1	3	10
30	12	1	4	3
31	3	4	8	1
32	6	8	5	1
33	3	1	6	2
34	3	8	6	1
35	3	8	7	6

Nodes	Coordinates			Boundary conditions			Solution
	X	Y	Z	u	v	w	u	v	w
1	0.249	0.342	0.192	-	-	-	0.000516	0.0005625	0.0004875
2	0.826	0.288	0.288	-	-	-	0.001114	0.000845	0.000845
3	0.85	0.649	0.263	-	-	-	0.001306	0.0012055	0.0010125
4	0.273	0.75	0.23	-	-	-	0.000763	0.0010015	0.0007415
5	0.32	0.25	0.643	-	-	-	0.0007665	0.0007315	0.000928
6	0.677	0.305	0.683	-	-	-	0.001171	0.000985	0.001174
7	0.788	0.693	0.644	-	-	-	0.0014565	0.001409	0.0013845
8	0.165	0.745	0.702	-	-	-	0.0008885	0.0011785	0.001157
9	0	0	0	0	0	0	0	0	0
10	1	0	0	0.001	0.0005	0.0005	0.001	0.0005	0.0005
11	1	1	0	0.0015	0.0015	0.001	0.0015	0.0015	0.001
12	0	1	0	0.0005	0.001	0.0005	0.0005	0.001	0.0005
13	0	0	1	0.0005	0.0005	0.001	0.0005	0.0005	0.001
14	1	0	1	0.0015	0.001	0.0015	0.0015	0.001	0.0015
15	1	1	1	0.002	0.002	0.002	0.002	0.002	0.002
16	0	1	1	0.001	0.0015	0.0015	0.001	0.0015	0.0015

Patch test for arbitrary three dimensional eight node element

Element	Nodes
1	9	1	4	12	13	5	8	16
2	9	10	2	1	13	14	6	5
3	2	10	11	3	6	14	15	7
4	12	4	3	11	16	8	7	15
5	5	6	7	8	13	14	15	16
6	9	10	11	12	1	2	3	4
7	1	2	3	4	5	6	7	8

Nodes	Coordinates			Boundary conditions			Solution
	X	Y	Z	u	v	w	u	v	w
1	0.249	0.342	0.192	-	-	-	0.000516	0.0005625	0.0004875
2	0.826	0.288	0.288	-	-	-	0.001114	0.000845	0.000845
3	0.85	0.649	0.263	-	-	-	0.001306	0.0012055	0.0010125
4	0.273	0.75	0.23	-	-	-	0.000763	0.0010015	0.0007415
5	0.32	0.186	0.643	-	-	-	0.0007345	0.0006675	0.000896
6	0.677	0.305	0.683	-	-	-	0.001171	0.000985	0.001174
7	0.788	0.693	0.644	-	-	-	0.0014565	0.001409	0.0013845
8	0.165	0.745	0.702	-	-	-	0.0008885	0.0011785	0.001157
9	0	0	0	0	0	0	0	0	0
10	1	0	0	0.001	0.0005	0.0005	0.001	0.0005	0.0005
11	1	1	0	0.0015	0.0015	0.001	0.0015	0.0015	0.001
12	0	1	0	0.0005	0.001	0.0005	0.0005	0.001	0.0005
13	0	0	1	0.0005	0.0005	0.001	0.0005	0.0005	0.001
14	1	0	1	0.0015	0.001	0.0015	0.0015	0.001	0.0015
15	1	1	1	0.002	0.002	0.002	0.002	0.002	0.002
16	0	1	1	0.001	0.0015	0.0015	0.001	0.0015	0.0015