A DGFEM for Nondivergence Form Elliptic Equations with Cordes Coefficients on Curved Domains

Abstract

In "I. Smears, E. Süli, \emph{Discontinuous Galerkin finite element approximation of nondivergence form elliptic equations with Cordés coefficients. SIAM J. Numer Anal., 51(4):2088-2106, 2013}" the authors designed and analysed a discontinuous Galerkin finite element method for the approximation of solutions to elliptic partial differential equations in nondivergence form. The results were proven, based on the assumption that the computational domain was convex and \emph{polytopal}. In this paper, we extend this framework, allowing for Lipschitz continuous domains with piecewise curved boundaries.