1 Introduction
2 STCG method for 2D wave equation
3 Error estimates of the STCG solutions
4 Numerical example
h
|
Error in
\(\boldsymbol{L^{2}}\)
|
Rate
|
Error in
\(\boldsymbol{H^{1}}\)
|
Rate
|
---|---|---|---|---|
1/8 | 4.8975e − 2 | 1.6055e − 0 | ||
1/16 | 1.2272e − 2 | 1.9967 | 8.0820e − 1 | 0.9902 |
1/32 | 3.0747e − 3 | 1.9968 | 4.0534e − 1 | 0.9956 |
1/64 | 7.6265e − 4 | 2.0113 | 2.0206e − 2 | 1.0043 |
h
|
Error in
\(\boldsymbol{L^{2}}\)
|
Rate
|
Error in
\(\boldsymbol{H^{1}}\)
|
Rate
|
---|---|---|---|---|
1/8 | 2.4889e − 2 | 8.0276e − 1 | ||
1/16 | 6.2303e − 3 | 1.9981 | 4.0410e − 1 | 0.9903 |
1/32 | 1.4268e − 3 | 2.1266 | 2.0268e − 1 | 0.9955 |
1/64 | 2.3105e − 4 | 2.6265 | 1.0109e − 1 | 1.0036 |
h
|
Error in
\(\boldsymbol{L^{2}(L^{2})}\)
|
Rate
|
Error in
\(\boldsymbol{L^{2}(H^{1})}\)
|
Rate
|
---|---|---|---|---|
1/8 | 6.4243e − 2 | 2.1045e − 0 | ||
1/16 | 1.6078e − 2 | 1.9985 | 1.0594e − 0 | 0.9902 |
1/32 | 4.0188e − 3 | 2.0003 | 5.3134e − 1 | 0.9956 |
1/64 | 9.8849e − 4 | 2.0235 | 2.6487e − 1 | 1.0043 |
h
|
Error in
\(\boldsymbol{L^{2}(L^{2})}\)
|
Rate
|
Error in
\(\boldsymbol{L^{2}(H^{1})}\)
|
Rate
|
---|---|---|---|---|
1/8 | 3.2219e − 2 | 1.0523e − 0 | ||
1/16 | 8.0528e − 3 | 2.0004 | 5.2971e − 1 | 0.9903 |
1/32 | 2.0065e − 3 | 2.0048 | 2.6567e − 1 | 0.9955 |
1/64 | 5.0324e − 4 | 1.9953 | 1.3247e − 1 | 1.0040 |
(
h
,
k
)
|
Error in
\(\boldsymbol{L^{2}}\)
|
Rate
|
(
h
,
k
)
|
Error in
\(\boldsymbol{H^{1}}\)
|
Rate
|
---|---|---|---|---|---|
(0.125,1/4) | 2.4620e − 2 | (1/8,1/2) | 8.0728e − 1 | ||
(0.0442,1/8) | 3.1414e − 3 | 2.9703 | (1/27,1/3) | 2.4231e − 1 | 2.9681 |
(0.0156,1/16) | 3.9093e − 4 | 3.0064 | (1/64,1/4) | 1.0114e − 1 | 3.0372 |
(
h
,
k
)
|
Error in
\(\boldsymbol{L^{2}}\)
|
Rate
|
(
h
,
k
)
|
Error in
\(\boldsymbol{H^{1}}\)
|
Rate
|
---|---|---|---|---|---|
(0.125,1/4) | 1.2556e − 2 | (1/8,1/2) | 4.0417e − 1 | ||
(0.0442,1/8) | 1.5500e − 3 | 3.0181 | (1/27,1/3) | 1.2116e − 1 | 2.9712 |
(0.0156,1/16) | 1.1918e − 4 | 3.7010 | (1/64,1/4) | 5.0577e − 2 | 3.0367 |
(
h
,
k
)
|
Error in
\(\boldsymbol{L^{2}(L^{2})}\)
|
Rate
|
(
h
,
k
)
|
Error in
\(\boldsymbol{L^{2}(H^{1})}\)
|
Rate
|
---|---|---|---|---|---|
(0.125,1/4) | 3.2246e − 2 | (1/8,1/2) | 1.0582e − 0 | ||
(0.0442,1/8) | 4.1121e − 3 | 2.9712 | (1/27,1/3) | 3.1763e − 1 | 2.9681 |
(0.0156,1/16) | 5.0685e − 4 | 3.0203 | (1/64,1/4) | 1.3257e − 1 | 3.0372 |
(
h
,
k
)
|
Error in
\(\boldsymbol{L^{2}(L^{2})}\)
|
Rate
|
(
h
,
k
)
|
Error in
\(\boldsymbol{L^{2}(H^{1})}\)
|
Rate
|
---|---|---|---|---|---|
(0.125,1/4) | 1.6141e − 2 | (1/8,1/2) | 5.2912e − 1 | ||
(0.0442,1/8) | 2.0566e − 3 | 2.9724 | (1/27,1/3) | 1.5882e − 1 | 2.9681 |
(0.0156,1/16) | 2.5788e − 4 | 2.9955 | (1/64,1/4) | 6.6294e − 2 | 3.0369 |