Smears, I;
Sueli, E;
(2013)
Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients.
SIAM: Journal on Numerical Analysis
, 51
(4)
pp. 2088-2106.
10.1137/120899613.
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Abstract
Nondivergence form elliptic equations with discontinuous coefficients do not generally possess 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 which satisfy the Cordès 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.
| Type: | Article |
|---|---|
| Title: | Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/120899613 |
| Publisher version: | http://dx.doi.org/10.1137/120899613 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, discontinuous Galerkin, hp-DGFEM, Cordes condition, nondivergence form, discontinuous coefficients, PDEs, finite element methods, CONVERGENCE, VERSION |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1572511 |
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