Second-order elliptic PDE with discontinuous boundary data

Houston, Paul and Wihler, Thomas P. (2009) Second-order elliptic PDE with discontinuous boundary data. IMA Journal of Numerical Analysis . ISSN 0272-4979 (Submitted)

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We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 15 Jan 2010 19:09
Last Modified: 04 May 2020 20:26

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