A note on the design of hp-version interior penalty discontinuous Galerkin finite element methods for degenerate problems
We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors or arbitrary form are covered in the theory present...
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| Aineistotyyppi: | Report |
| Julkaistu: |
Unspecified
2005
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| Yhteenveto: | We consider a variant of the hp-version interior penalty discontinuous Galerkin finite element method (IP-DGFEM) for second order problems of degenerate type. We do not assume uniform ellipticity of the diffusion tensor. Moreover, diffusion tensors or arbitrary form are covered in the theory presented. A new, refined recipe for the choice of the discontinuity-penalisation parameter (that is present in the formlation of the IP-DGFEM) is given. Making use of the recently introduced augmented Sobolev space framework, we prove an hp-optimal error bound in the energy norm and an h-optimal and slightly p-suboptimal (by only half an order of p) bound in the L2 norm, provided that the solution belongs to an augmented Sobolev space. |
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