The Mathematical Institute, University of Oxford, Eprints Archive

Discontinuous Galerkin finite element approximation of non-divergence form elliptic equations with Cordes coefficients

Smears, Iain and Suli, Endre (2012) Discontinuous Galerkin finite element approximation of non-divergence form elliptic equations with Cordes coefficients. Technical Report. Unspecified. (Submitted)

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Abstract

Non-divergence form elliptic equations with discontinuous coefficients do not generally posses a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new $hp$-version discontinuous Galerkin finite element method for a class of these problems that satisfy the Cordes condition. It is shown that the method exhibits a convergence rate that is optimal with respect to the mesh size $h$ and suboptimal with respect to the polynomial degree $p$ by only half an order. Numerical experiments demonstrate the accuracy of the method and illustrate the potential of exponential convergence under $hp$-refinement for problems with discontinuous coefficients and nonsmooth solutions.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Partial differential equations
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1623
Deposited By:Lotti Ekert
Deposited On:21 Nov 2012 09:17
Last Modified:21 Nov 2012 09:17

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