Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity


Autoria(s): Georgoulis, Emmanuil H.; Hall, Edward; Houston, Paul
Resumo

We consider the a posteriori error analysis and hp-adaptation strategies for hp-version interior penalty discontinuous Galerkin methods for second-order partial differential equations with nonnegative characteristic form on anisotropically refined computational meshes with anisotropically enriched elemental polynomial degrees. In particular, we exploit duality based hp-error estimates for linear target functionals of the solution and design and implement the corresponding adaptive algorithms to ensure reliable and efficient control of the error in the prescribed functional to within a given tolerance. This involves exploiting both local isotropic and anisotropic mesh refinement and isotropic and anisotropic polynomial degree enrichment. The superiority of the proposed algorithm in comparison with standard hp-isotropic mesh refinement algorithms and an h-anisotropic/p-isotropic adaptive procedure is illustrated by a series of numerical experiments.

Formato

application/pdf

Identificador

http://eprints.nottingham.ac.uk/670/1/DG_on_anis_mesh_functionalsII.pdf

Georgoulis, Emmanuil H. and Hall, Edward and Houston, Paul Discontinuous Galerkin Methods on hp-Anisotropic Meshes II: A Posteriori Error Analysis and Adaptivity. Applied Numerical Mathematics . (Submitted)

Idioma(s)

en

Relação

http://eprints.nottingham.ac.uk/670/

Tipo

Article

NonPeerReviewed