Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordès coefficients
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 th...
| প্রধান লেখক: | , |
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| বিন্যাস: | Journal article |
| ভাষা: | English |
| প্রকাশিত: |
Society for Industrial and Applied Mathematics
2013
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| সংক্ষিপ্ত: | 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. |
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