conservation-laws / ryujin

High-performance high-order finite element solver for hyperbolic conservation equations
https://conservation-laws.org
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dG Infrastructure, Part 6 #101

Closed tamiko closed 3 months ago

tamiko commented 3 months ago

Use consistent mass matrix for dG. This improves things considerably:

Lumped:
  #dofs    L1 error          L2 error          Linf error
-------  ----------  ----  ----------  ----  ------------  ----
    256  0.121101          0.240558             1.3169
   1024  0.0569684   1.09  0.128049    0.91     0.708533   0.89
   4096  0.0190687   1.58  0.0454181   1.5      0.243257   1.54
  16384  0.00534926  1.83  0.0131967   1.78     0.0654211  1.89
  65536  0.00139235  1.94  0.00347455  1.93     0.0166031  1.98

Neumann:
  #dofs     L1 error           L2 error          Linf error
-------  -----------  ----  -----------  ----  ------------  ----
    256  0.0899719          0.173239             0.974782
   1024  0.0307984    1.55  0.0694108    1.32    0.426135    1.19
   4096  0.00885452   1.8   0.0212493    1.71    0.128029    1.73
  16384  0.00232961   1.93  0.00575481   1.88    0.0321078   2.0
  65536  0.000590042  1.98  0.00146795   1.97    0.00794425  2.01

Consistent:
  #dofs     L1 error           L2 error          Linf error
-------  -----------  ----  -----------  ----  ------------  ----
    256  0.0617453          0.105298             0.664432
   1024  0.0132785    2.22  0.0276867    1.93    0.207695    1.68
   4096  0.00282365   2.23  0.00659583   2.07    0.0537336   1.95
  16384  0.000633277  2.16  0.00154839   2.09    0.0142595   1.91
  65536  0.000147882  2.1   0.000368647  2.07    0.00288742  2.3