Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method | Zendy

Manolis K. Georgoulis | Zendy

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Optimal error estimates for the hp-version interior penalty discontinuous Galerkin finite element method

Author(s) -

Manolis K. Georgoulis

Publication year - 2004

Publication title -

ima journal of numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.672

H-Index - 66

eISSN - 1464-3642

pISSN - 0272-4979

DOI - 10.1093/imanum/drh014

Subject(s) - mathematics , penalty method , discontinuous galerkin method , sobolev space , finite element method , degree of a polynomial , norm (philosophy) , galerkin method , space (punctuation) , mathematical analysis , polynomial , function (biology) , mathematical optimization , computer science , physics , evolutionary biology , biology , political science , law , thermodynamics , operating system

We consider the hp-version interior penalty discontinuous Galerkin finite-element method (hp-DGFEM) for second-order linear reaction–diffusion equations. To the best of our knowledge, the sharpest known error bounds for the hp-DGFEM are due to Rivière et al.(1999, Comput. Geosci., 3, 337–360) and Houston et al.(2002, SIAM J. Numer. Anal., 99, 2133–2163). These are optimal with respect to the meshs...

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