An elliptic problem in a domain with an external cusp: theoretical and numerical aspects

G. ACOSTA; G. ARMENTANO; R. G. DURÁN; A. LOMBARDI

Congreso; International Conference in Approximation Methods for Design and Control; 2005

We show that even for regular solutions, the finite element method may need adapted meshes on singular domains. Indeed, for the Poisson problem in a domain with an external cusp we present some examples where uniform meshes deliver discrete solutions of  with suboptimal order of convergence. Finally we show that it is possible to recover optimal order of convergence by means of particular adapted graded meshes.