TY  - JOUR
ID  - discovery1572511
UR  - http://dx.doi.org/10.1137/120899613
N2  - 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.
Y1  - 2013/01/01/
JF  - SIAM: Journal on Numerical Analysis
A1  - Smears, I
A1  - Sueli, E
PB  - SIAM PUBLICATIONS
SP  - 2088
VL  - 51
EP  - 2106
IS  - 4
AV  - public
SN  - 1095-7170
TI  - Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients
KW  - Science & Technology
KW  -  Physical Sciences
KW  -  Mathematics
KW  -  Applied
KW  -  Mathematics
KW  -  discontinuous Galerkin
KW  -  hp-DGFEM
KW  -  Cordes condition
KW  -  nondivergence form
KW  -  discontinuous coefficients
KW  -  PDEs
KW  -  finite element methods
KW  -  CONVERGENCE
KW  -  VERSION
N1  - This version is the version of record. For information on re-use, please refer to the publisher?s terms and conditions.
ER  -