Stabilised finite element methods for ill-posed problems with conditional stability
Abstract
In this paper we discuss the adjoint stabilised finite element method introduced in, E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive and ill-posed problems. Part I: elliptic equations, SIAM Journal on Scientific Computing, and how it may be used for the computation of solutions to problems for which the standard stability theory given by the Lax-Milgram Lemma or the Babuska-Brezzi Theorem fails. We pay particular attention to ill-posed problems that have some conditional stability property and prove (conditional) error estimates in an abstract framework. As a model problem we consider the elliptic Cauchy problem and provide a complete numerical analysis for this case. Some numerical examples are given to illustrate the theory.
Cite
@article{arxiv.1512.02837,
title = {Stabilised finite element methods for ill-posed problems with conditional stability},
author = {Erik Burman},
journal= {arXiv preprint arXiv:1512.02837},
year = {2015}
}
Comments
Accepted in the proceedings from the EPSRC Durham Symposium Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations