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

no code implementations • 9 Feb 2021 • Zelalem Arega Worku, David W. Zingg

Sufficient conditions for stability of adjoint consistent discretizations with the narrow-stencil generalized SBP operators are presented.

Numerical Analysis Numerical Analysis 65M06, 65M12, 65N06, 65N12

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

no code implementations • 14 Dec 2020 • Zelalem Arega Worku, David W. Zingg

For SATs leading to primal and adjoint consistent discretizations, the error in output functionals is shown to be of order $h^{2p}$ when a degree $p$ multidimensional SBP operator is used to discretize the spatial derivatives.

Numerical Analysis Numerical Analysis 65M06 (Primary), 65M12, 65N30 (Secondary)