A new stabilized finite element method for reaction-diffusion problems: The Source Stabilized Petrov-Galerkin Method

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DOIResolve DOI: http://doi.org/10.1002/nme2324
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TypeArticle
Journal titleInternational Journal for Numerical Methods in Engineering
Volume75
Pages16071630; # of pages: 23
Subjectstabilized finite elements; source stabilization; Taylor series expansion; Petrov–Galerkin; oscillation-free solutions
AbstractThis paper proposes a new stabilized finite element method to solve singular diffusion problems described by the modified Helmholtz operator. The Galerkin method is known to produce spurious oscillations for low diffusion and various alternatives were proposed to improve the accuracy of the solution. The mostly used methods are the well-known Galerkin least squares and Galerkin gradient least squares (GGLS). The GGLS method yields the exact nodal solution in the one-dimensional case and for a uniform mesh. However, the behavior of the method deteriorates slightly in the multi-dimensional case and for nonuniform meshes. In this work we propose a new stabilized finite element method that leads to improved accuracy for multi-dimensional problems. For the one-dimensional case, the new method leads to the same results as the GGLS method and hence provides exact nodal solutions to the problem on uniform meshes. The proposed method is a Galerkin discretization used to solve a modified equation that includes a term depending on the gradient of the original partial differential equation.
Publication date
LanguageEnglish
AffiliationNational Research Council Canada (NRC-CNRC); NRC Industrial Materials Institute
Peer reviewedYes
NRC number50216
NPARC number15993414
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Record identifier7bc30fb6-336b-4fee-a5c0-35a2ae0d943d
Record created2010-11-02
Record modified2016-05-09
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