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Patch‐wise local projection stabilized finite element methods for convection–diffusion–reaction problems
Author(s) -
Dond Asha K.,
Gudi Thirupathi
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22317
Subject(s) - mathematics , finite element method , projection (relational algebra) , mixed finite element method , galerkin method , discontinuous galerkin method , a priori and a posteriori , norm (philosophy) , dirichlet boundary condition , mathematical analysis , convection–diffusion equation , extended finite element method , boundary value problem , algorithm , philosophy , physics , epistemology , political science , law , thermodynamics
In this article, we develop patch‐wise local projection‐stabilized conforming and nonconforming finite element methods for the convection–diffusion–reaction problems. It is a composition of the standard Galerkin finite element method, the patch‐wise local projection stabilization, and weakly imposed Dirichlet boundary conditions on the discrete solution. In this paper, a priori error analysis is established with respect to a patch‐wise local projection norm for the conforming and the nonconforming finite element methods. The numerical experiments confirm the efficiency of the proposed stabilization technique and validate the theoretical convergence rates.