A dual consistent finite difference method with narrow stencil second derivative operators
Abstract
We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order summation by parts operators, combined with a boundary procedure using penalties (SBP-SAT). Recently it was shown that SBP-SAT finite difference methods can yield superconvergent functional output if the boundary conditions are imposed such that the discretization is dual consistent. We generalize these results so that they include a broader range of boundary conditions and penalty parameters. The results are also generalized to hold for narrow-stencil second derivative operators. The derivations are supported by numerical experiments.
Cite
@article{arxiv.1611.06187,
title = {A dual consistent finite difference method with narrow stencil second derivative operators},
author = {Sofia Eriksson},
journal= {arXiv preprint arXiv:1611.06187},
year = {2017}
}