Professor PAUL HOUSTON PAUL.HOUSTON@NOTTINGHAM.AC.UK
Head of School (Professor of Computational and Applied Maths)
Second-order elliptic PDE with discontinuous boundary data
Houston, Paul; Wihler, Thomas P.
Authors
Thomas P. Wihler
Abstract
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.
Citation
Houston, P., & Wihler, T. P. Second-order elliptic PDE with discontinuous boundary data. Manuscript submitted for publication
Journal Article Type | Article |
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Deposit Date | Jan 15, 2010 |
Peer Reviewed | Not Peer Reviewed |
Public URL | https://nottingham-repository.worktribe.com/output/1013509 |
Files
houston_wihler_imajna.pdf
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PDF
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