The Mathematical Institute, University of Oxford, Eprints Archive

Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case

Houston, P. and Robson, Janice A. and Suli, Endre (2004) Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case. Technical Report. Unspecified. (Submitted)

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Abstract

We develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1176
Deposited By:Lotti Ekert
Deposited On:18 May 2011 08:11
Last Modified:18 May 2011 08:11

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