Anisotropic mesh refinement in stabilized Galerkin methods | Zendy

Thomas Apel | Zendy; Gert Lube | Zendy

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Anisotropic mesh refinement in stabilized Galerkin methods

Author(s) -

Thomas Apel,

Gert Lube

Publication year - 1996

Publication title -

numerische mathematik

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.214

H-Index - 90

eISSN - 0945-3245

pISSN - 0029-599X

DOI - 10.1007/s002110050216

Subject(s) - galerkin method , mathematics , finite element method , isotropy , polygon mesh , boundary layer , mathematical analysis , anisotropy , numerical analysis , boundary (topology) , convection–diffusion equation , geometry , mechanics , physics , quantum mechanics , thermodynamics

Summary. The numerical solution of a convection-diffusion-reaction model problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least-square type accomodates diffusion-dominated as well as convection- and/or reaction-dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.

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