Research Article
A Third Order Accurate Cellwise Relaxation Implicit Discontinuous Galerkin Scheme for Unstructured Hybrid Meshes
Table 1
Computed results for the parabolic equation using 2nd, 3rd, and 4th order schemes.
| | Cell aspect ratio is 1 | Cell aspect ratio is 1000 | | Mesh-1a | Mesh-1b | Mesh-1c | Mesh-2a | Mesh-2b | Mesh-2c |
| Time steps needed for machine zero convergence | | | | | | | 2nd order | 3210 | 12320 | 46890 | 6110 | 22880 | 86260 | 3rd order | 5990 | 22680 | 85880 | 11800 | 44650 | 168060 | 4th order | 9430 | 35650 | 134830 | 17270 | 65340 | 247390 | CPU time per one time step | | | | | | | 2nd order | 0.0099 s | 0.0527 s | 0.3961 s | 0.0104 s | 0.0528 s | 0.4005 s | 3rd order | 0.0361 s | 0.2212 s | 1.8564 s | 0.0359 s | 0.2256 s | 1.8497 s | 4th order | 0.1989 s | 1.3447 s | 10.520 s | 0.1962 s | 1.3376 s | 10.482 s | Log10(Error) of converged solutions | | | | | | | 2nd order | −2.5600 | −4.8282 | −6.2279 | −2.7419 | −4.7185 | −7.0051 | 3rd order | −3.1516 | −5.7300 | −7.3960 | −3.3393 | −5.5940 | −8.2653 | 4th order | −3.7487 | −6.6345 | −8.5852 | −3.9279 | −6.4839 | −9.5030 | Attained spatial accuracy | | | | | | | 2nd order | 1.96979 | 1.97443 | 3rd order | 2.93233 | 3.00013 | 4th order | 4.14892 | 3.91538 |
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