Interior penalty discontinuous Galerkin method on very general polygonal and polyhedral meshes

• Autores: Lin Mu, Junping Wang, Yanqiu Wang, Xiu Ye
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 255, Nº 1, 2014, págs. 432-440
• Idioma: inglés
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• Resumen

  • This paper provides a theoretical foundation for interior penalty discontinuous Galerkin methods for second-order elliptic equations on very general polygonal or polyhedral meshes. The mesh can be composed of any polygons or polyhedra that satisfy certain shape regularity conditions characterized in a recent paper by two of the authors, Wang and Ye (2012) [11]. The usual H1-conforming finite element methods on such meshes are either very complicated or impossible to implement in practical computation. The interior penalty discontinuous Galerkin method provides a simple and effective alternative approach which is efficient and robust. Results with such general meshes have important application in computational sciences.