A dual Petrov-Galerkin finite element method for the convection-diffusion equation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Pages (from-to)1513-1529
Journal / PublicationComputers and Mathematics with Applications
Volume68
Issue number11
Online published28 Jul 2014
Publication statusPublished - Dec 2014

Abstract

We present a minimum-residual finite element method (based on a dual Petrov-Galerkin formulation) for convection-diffusion problems in a higher order, adaptive, continuous Galerkin setting. The method borrows concepts from both the Discontinuous Petrov-Galerkin (DPG) method by Demkowicz and Gopalakrishnan (2011) and the method of variational stabilization by Cohen, Dahmen, and Welper (2012), and it can also be interpreted as a variational multiscale method in which the fine-scales are defined through a dual-orthogonality condition. A key ingredient in the method is the proper choice of dual norm used to measure the residual, and we present two choices which are observed to be robust in both convection and diffusion-dominated regimes, as well as a proof of stability for quasi-uniform meshes and a method for the weak imposition of boundary conditions. Numerically obtained convergence rates in 2D are reported, and benchmark numerical examples are given to illustrate the behavior of the method.

Research Area(s)

  • Convection-diffusion, High order, Petrov-Galerkin, Stabilized finite elements