Burman, E; (2013) Stabilized Finite Element Methods for Nonsymmetric, Noncoercive, and Ill-Posed Problems. Part I: Elliptic Equations. SIAM Journal on Scientific Computing , 35 (6) A2752 - A2780. 10.1137/130916862.

PDF 91686.pdf Available under License : See the attached licence file. Download (541kB)

Abstract

In this paper we propose a new method to stabilize nonsymmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilized finite element method. Both stabilization of the element residual and of the jumps of certain derivatives of the discrete solution over element faces may be used. Under the assumption of well-posedness of the partial differential equation and its associated adjoint problem we prove optimal error estimates in $H^1$ and $L^2$ norms in an abstract framework. Some examples of problems that are neither symmetric nor coercive but that enter the abstract framework are given. First we treat indefinite convection-diffusion equations with nonsolenoidal transport velocity and either pure Dirichlet conditions or pure Neumann conditions and then a Cauchy problem for the Helmholtz operator. Some numerical illustrations are given. Read More: http://epubs.siam.org/doi/abs/10.1137/130916862

Download activity - last month

Export as JSONXMLCSV

Download activity - last 12 months

Export as CSVXMLJSON

Downloads by country - last 12 months

Export as CSVXMLJSON

Archive Staff Only

View Item