The Mathematical Institute, University of Oxford, Eprints Archive

Optimal Error Estimates for the hp–Version Interior Penalty Discontinuous Galerkin Finite Element Method

Georgoulis, Emmanuil H. and Suli, Endre (2003) Optimal Error Estimates for the hp–Version Interior Penalty Discontinuous Galerkin Finite Element Method. Technical Report. Unspecified. (Submitted)

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Abstract

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for second-order linear reaction-diffusion equations. To the best of our knowledge, the sharpest known error bounds for the hp-DGFEM are due to Riviere, Wheeler and Girault [9] and due to Houston, Schwab and Süli [6] which are optimal with respect to the meshsize h but suboptimal with respect to the polynomial degree p by half an order of p. We present improved error bounds in the energy norm, by introducing a new function space framework. More specifically, assuming that the solutions belong element-wise to an augmented Sobolev space, we deduce hp-optimal error bounds.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1201
Deposited By:Lotti Ekert
Deposited On:18 May 2011 08:11
Last Modified:08 Oct 2012 13:35

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