Patch-wise local projection stabilized finite element methods for convection–diffusion–reaction problems

Dond, AK and Gudi, T (2019) Patch-wise local projection stabilized finite element methods for convection–diffusion–reaction problems. In: Numerical Methods for Partial Differential Equations, 35 (2). pp. 638-663.

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Abstract

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.

Item Type:	Journal Article
Publication:	Numerical Methods for Partial Differential Equations
Publisher:	John Wiley and Sons Inc.
Additional Information:	The copyright for this article belongs to John Wiley and Sons Inc.
Keywords:	Boundary conditions; Diffusion; Error analysis; Incompressible flow; Stabilization, Dirichlet boundary condition; Galerkin finite element methods; Local projection stabilizations; Local projections; Nonconforming finite element method; Priori error analysis; Stabilization techniques; Stabilized finite element methods, Finite element method
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	15 Dec 2022 08:03
Last Modified:	15 Dec 2022 08:03
URI:	https://eprints.iisc.ac.in/id/eprint/78319

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