Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts Discretizations

We analyze the stability and functional superconvergence of discretizations diffusion problems with narrow-stencil second-derivative generalized summation-by-parts (SBP) operators coupled simultaneous approximation terms (SATs). Provided that primal adjoint solutions are sufficiently smooth SBP-SAT discretization is consistent, we show linear functionals associated steady problem superconverge at a rate $ 2p when degree p+1 or p wide-stencil SBP operator used for spatial discretization. Sufficient conditions consistent presented. The analysis assumes nullspace consistency invertibility matrix approximating first derivative element boundaries. theoretical results verified by numerical experiments one-dimensional Poisson problem.