A DGFEM for Nondivergence Form Elliptic Equations with Cordes Coefficients on Curved Domains
Provides a theoretical foundation for applying this method to more realistic geometries, which is incremental for numerical analysis researchers.
Extended a discontinuous Galerkin finite element method for nondivergence form elliptic equations with Cordes coefficients from polytopal to curved domains, proving convergence under minimal regularity assumptions.
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.