Output error estimation for summation-by-parts finite-difference schemes

Authors:
J. E. Hicken
Affiliations:
Department of Aeronautics & Astronautics, Durand 250, 496 Lomita Mall, Stanford, CA 94305-4035, United States
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

The paper develops a posteriori error estimates of integral output functionals for summation-by-parts finite-difference methods. The error estimates are based on the adjoint-weighted residual method and take advantage of a variational interpretation of summation-by-parts discretizations. The estimates are computed on a fixed grid and do not require an embedded grid or explicit interpolation operators. For smooth boundary-value problems containing first and second derivatives the error estimates converge to the exact error as the mesh is refined. The theory is verified using linear boundary-value problems and the Euler equations.