Unstructured, curved elements for the two-dimensional high order discontinuous control-volume/finite-element method

Quadrilateral and triangular elements with curved edges are developed in the framework of spectral, discon- tinuous, hybrid control-volume/finite-element method for elliptic problems. In order to accommodate hybrid meshes, encompassing both triangular and quadrilateral elements, one single mapping is used. The scheme is applied to two-dimensional problems with discontinuous, anisotropic diffusion coefficients, and the expo- nential convergence of the method is verified in the presence of curved geometries.