Simultaneous approximation terms and functional accuracy for diffusion problems discretized with multidimensional summation-by-parts operators

Several types of simultaneous approximation term (SAT) for diffusion problems discretized with diagonal-norm multidimensional summation-by-parts (SBP) operators are analyzed based on a common framework. Conditions under which the SBP-SAT discretizations consistent, conservative, adjoint and energy stable presented. For SATs leading to primal consistent discretizations, error in output functionals is shown be order h2p when degree p SBP operator used discretize spatial derivatives. SAT penalty coefficients corresponding various discontinuous Galerkin fluxes developed elliptic partial differential equations identified. We demonstrate that original method Bassi Rebay, modified symmetric interior equivalent implemented diagonal-E have diagonal norm matrix, e.g., Legendre-Gauss-Lobatto one space dimension. Similarly, local compact schemes this family operators. The analysis remains valid curvilinear grids if ?p+1 bijective polynomial mapping from reference physical elements used. Numerical experiments two-dimensional Poisson problem support theoretical results.