@article{discovery1572511,
       publisher = {SIAM PUBLICATIONS},
          volume = {51},
           month = {January},
            note = {This version is the version of record. For information on re-use, please refer to the publisher's terms and conditions.},
           pages = {2088--2106},
         journal = {SIAM: Journal on Numerical Analysis},
          number = {4},
            year = {2013},
           title = {Discontinuous Galerkin Finite Element Approximation of Nondivergence Form Elliptic Equations With Cordes Coefficients},
            issn = {1095-7170},
        keywords = {Science \& Technology, Physical Sciences, Mathematics, Applied, Mathematics, discontinuous Galerkin, hp-DGFEM, Cordes condition, nondivergence form, discontinuous coefficients, PDEs, finite element methods, CONVERGENCE, VERSION},
          author = {Smears, I and Sueli, E},
             url = {http://dx.doi.org/10.1137/120899613},
        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 Cord{\`e}s 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.}
}