03 March 2022 10:55:29 PM
FEM1D_BVP_LINEAR_TEST
C version
Test the FEM1D_BVP_LINEAR library.
TEST00
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A(X) = 1.0
C(X) = 1.0
F(X) = X
U(X) = X - SINH(X) / SINH(1)
Number of nodes = 11
I X U Uexact Error
0 0.000000 0.000000 0.000000 0.000000e+00
1 0.100000 0.014777 0.014766 1.101255e-05
2 0.200000 0.028701 0.028680 2.142298e-05
3 0.300000 0.040909 0.040878 3.061605e-05
4 0.400000 0.050521 0.050483 3.794995e-05
5 0.500000 0.056633 0.056591 4.274259e-05
6 0.600000 0.058304 0.058260 4.425718e-05
7 0.700000 0.054549 0.054507 4.168701e-05
8 0.800000 0.044329 0.044295 3.413914e-05
9 0.900000 0.026539 0.026518 2.061676e-05
10 1.000000 0.000000 0.000000 0.000000e+00
l1 norm of error = 2.58586e-05
L2 norm of error = 0.000426196
Seminorm of error = 0.0156388
Max norm of error = 0.0011594
TEST01
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A1(X) = 1.0
C1(X) = 0.0
F1(X) = X * ( X + 3 ) * exp ( X )
U1(X) = X * ( 1 - X ) * exp ( X )
Number of nodes = 11
I X U Uexact Error
0 0.000000 0.000000 0.000000 0.000000e+00
1 0.100000 0.099466 0.099465 1.334229e-07
2 0.200000 0.195425 0.195424 2.475629e-07
3 0.300000 0.283471 0.283470 3.394330e-07
4 0.400000 0.358038 0.358038 4.056126e-07
5 0.500000 0.412181 0.412180 4.421874e-07
6 0.600000 0.437309 0.437309 4.446805e-07
7 0.700000 0.422888 0.422888 4.079761e-07
8 0.800000 0.356087 0.356087 3.262308e-07
9 0.900000 0.221364 0.221364 1.927749e-07
10 1.000000 0.000000 0.000000 0.000000e+00
l1 norm of error = 2.67262e-07
L2 norm of error = 0.00400665
Seminorm of error = 0.138667
Max norm of error = 0.012139
TEST02
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A2(X) = 1.0
C2(X) = 2.0
F2(X) = X * ( 5 - X ) * exp ( X )
U2(X) = X * ( 1 - X ) * exp ( X )
Number of nodes = 11
I X U Uexact Error
0 0.000000 0.000000 0.000000 0.000000e+00
1 0.100000 0.099598 0.099465 1.321791e-04
2 0.200000 0.195686 0.195424 2.610606e-04
3 0.300000 0.283852 0.283470 3.818454e-04
4 0.400000 0.358526 0.358038 4.876318e-04
5 0.500000 0.412749 0.412180 5.689040e-04
6 0.600000 0.437921 0.437309 6.129042e-04
7 0.700000 0.423491 0.422888 6.028696e-04
8 0.800000 0.356604 0.356087 5.171057e-04
9 0.900000 0.221692 0.221364 3.278658e-04
10 1.000000 0.000000 0.000000 0.000000e+00
l1 norm of error = 0.000353851
L2 norm of error = 0.00369835
Seminorm of error = 0.138675
Max norm of error = 0.0119751
TEST03
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A3(X) = 1.0
C3(X) = 2.0 * X
F3(X) = - X * ( 2 * X * X - 3 * X - 3 ) * exp ( X )
U3(X) = X * ( 1 - X ) * exp ( X )
Number of nodes = 11
I X U Uexact Error
0 0.000000 0.000000 0.000000 0.000000e+00
1 0.100000 0.099549 0.099465 8.350349e-05
2 0.200000 0.195591 0.195424 1.664831e-04
3 0.300000 0.283718 0.283470 2.473411e-04
4 0.400000 0.358361 0.358038 3.227375e-04
5 0.500000 0.412567 0.412180 3.868178e-04
6 0.600000 0.437739 0.437309 4.302058e-04
7 0.700000 0.423327 0.422888 4.386892e-04
8 0.800000 0.356478 0.356087 3.914985e-04
9 0.900000 0.221623 0.221364 2.590522e-04
10 1.000000 0.000000 0.000000 0.000000e+00
l1 norm of error = 0.000247848
L2 norm of error = 0.00377892
Seminorm of error = 0.138671
Max norm of error = 0.0120095
TEST04
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A4(X) = 1.0 + X * X
C4(X) = 0.0
F4(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X )
U4(X) = X * ( 1 - X ) * exp ( X )
Number of nodes = 11
I X U Uexact Error
0 0.000000 0.000000 0.000000 0.000000e+00
1 0.100000 0.099820 0.099465 3.548374e-04
2 0.200000 0.196115 0.195424 6.903995e-04
3 0.300000 0.284455 0.283470 9.850737e-04
4 0.400000 0.359254 0.358038 1.215952e-03
5 0.500000 0.413540 0.412180 1.359969e-03
6 0.600000 0.438703 0.437309 1.394547e-03
7 0.700000 0.424186 0.422888 1.297708e-03
8 0.800000 0.357134 0.356087 1.047774e-03
9 0.900000 0.221987 0.221364 6.228182e-04
10 1.000000 0.000000 0.000000 0.000000e+00
l1 norm of error = 0.000815371
L2 norm of error = 0.00338872
Seminorm of error = 0.138705
Max norm of error = 0.0118277
TEST05
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A5(X) = 1.0 + X * X for X <= 1/3
= 7/9 + X for 1/3 < X
C5(X) = 0.0
F5(X) = ( X + 3 X^2 + 5 X^3 + X^4 ) * exp ( X )
for X <= 1/3
= ( - 1 + 10/3 X + 43/9 X^2 + X^3 ) .* exp ( X )
for 1/3 <= X
U5(X) = X * ( 1 - X ) * exp ( X )
Number of nodes = 11
I X U Uexact Error
0 0.000000 0.000000 0.000000 0.000000e+00
1 0.100000 0.099981 0.099465 5.151509e-04
2 0.200000 0.196432 0.195424 1.007893e-03
3 0.300000 0.284924 0.283470 1.453835e-03
4 0.400000 0.359566 0.358038 1.528433e-03
5 0.500000 0.413603 0.412180 1.422913e-03
6 0.600000 0.438574 0.437309 1.265587e-03
7 0.700000 0.423939 0.422888 1.051364e-03
8 0.800000 0.356861 0.356087 7.740815e-04
9 0.900000 0.221791 0.221364 4.264543e-04
10 1.000000 0.000000 0.000000 0.000000e+00
l1 norm of error = 0.000858701
L2 norm of error = 0.00349352
Seminorm of error = 0.138709
Max norm of error = 0.0119258
TEST06
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
A6(X) = 1.0
C6(X) = 0.0
F6(X) = pi*pi*sin(pi*X)
U6(X) = sin(pi*x)
Compute l1norm, L2norm and seminorm of error for various N.
N l1 error L2 error Seminorm error Maxnorm error
11 3.90303e-06 0.00579769 0.201186 0.0121534
21 2.56142e-07 0.0014528 0.100697 0.00307274
41 1.64086e-08 0.000363412 0.0503613 0.000770343
81 1.03833e-09 9.08662e-05 0.0251823 0.000192721
161 6.52875e-11 2.27174e-05 0.0125913 4.81886e-05
TEST07
Solve -( A(x) U'(x) )' + C(x) U(x) = F(x)
for 0 < x < 1, with U(0) = U(1) = 0.
Becker/Carey/Oden Example
Compute l1 norm, L2 norm and seminorm of error for various N.
N l1 error L2 error Seminorm error Maxnorm error
11 0.0105234 0.0548944 2.11962 0.272576
21 0.00468867 0.0151701 1.06991 0.0664751
41
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C 代码 应用有限元法计算出的解决方案和精确的解决方案 具有 L2 和半范数误差.rar
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C 代码 应用有限元法计算出的解决方案和精确的解决方案 具有 L2 和半范数误差.rar (10个子文件)
fem1d_bvp_linear_test
data.txt 275B
fem1d_bvp_linear_test.sh 461B
fem1d_bvp_linear_test.txt 12KB
commands_l2.txt 374B
commands_mx.txt 375B
fem1d_bvp_linear_test.c 61KB
commands_h1.txt 374B
fem1d_bvp_linear
fem1d_bvp_linear.h 758B
fem1d_bvp_linear.sh 244B
fem1d_bvp_linear.c 22KB
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