Paul Houston Paul.Houston@nottingham.ac.uk
Second-order elliptic PDE with discontinuous boundary data
Houston, Paul; Wihler, Thomas P.
Thomas P. Wihler email@example.com
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.
|Journal Article Type||Article|
|Journal||IMA Journal of Numerical Analysis|
|Publisher||Oxford University Press (OUP)|
|Peer Reviewed||Not Peer Reviewed|
|APA6 Citation||Houston, P., & Wihler, T. P. Second-order elliptic PDE with discontinuous boundary data. Manuscript submitted for publication|
|Copyright Statement||Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf|
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf
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