A Postprocessing Finite Element Strategy for Poisson’s Equation in Polygonal Domains: Computing the Stress Intensity Factors

Abstract

We present a new finite element algorithm for computing the stress intensity factors and the solution of boundary value problems for the Poisson equation in two-dimensional domains with corners. The method makes use of an explicit expression for the stress intensity factors in terms of the function of the right hand side, the solution of the boundary value problem and smooth cutoff functions to compute from an initial finite element solution approximations of the stress intensity factors. The computed values of the stress intensity factors are then used for post processing the finite element solution and the approximated stress intensity factors. The algorithm leads to good approximations of both stress intensity factors and the finite element solution of the boundary value problem on quasi regular meshes. The results are illustrated by numerical experiments.KeywordsStress Intensity FactorElement SolutionCutoff FunctionElliptic BoundaryConvergence OrderThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.