Convergence of Summation-by-Parts Finite Difference Methods for the Wave Equation
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DOI: 10.1007/s10915-016-0297-3
Abstract: When using a finite difference method to solve a time dependent partial differential equation, the truncation error is often larger at a few grid points near a boundary or grid interface than in the interior.… read more here.
Keywords: summation parts; convergence; equation; finite difference ... See more keywords
An Entropy Stable h / p Non-Conforming Discontinuous Galerkin Method with the Summation-by-Parts Property
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DOI: 10.1007/s10915-018-0733-7
Abstract: This work presents an entropy stable discontinuous Galerkin (DG) spectral element approximation for systems of non-linear conservation laws with general geometric (h) and polynomial order (p) non-conforming rectangular meshes. The crux of the proofs presented… read more here.
Keywords: summation parts; entropy stable; discontinuous galerkin; non ... See more keywords
Extension of Tensor-Product Generalized and Dense-Norm Summation-by-Parts Operators to Curvilinear Coordinates
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DOI: 10.1007/s10915-019-01011-3
Abstract: AbstractMethodologies are presented that enable the construction of provably linearly stable and conservative high-order discretizations of partial differential equations in curvilinear coordinates based on generalized summation-by-parts operators, including operators with dense-norm matrices. Specifically, three approaches… read more here.
Keywords: parts operators; curvilinear coordinates; dense norm; summation parts ... See more keywords
Superconvergent Functional Estimates from Tensor-Product Generalized Summation-by-Parts Discretizations in Curvilinear Coordinates
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DOI: 10.1007/s10915-020-01147-7
Abstract: We investigate superconvergent functional estimates in curvilinear coordinates for diagonal-norm tensor-product generalized summation-by-parts operators. We show that interpolation/extrapolation operators of degree greater than or equal to 2 p are required to preserve at least 2… read more here.
Keywords: generalized summation; summation parts; functional estimates; superconvergent functional ... See more keywords
A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions
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DOI: 10.1007/s10915-021-01454-7
Abstract: Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical… read more here.
Keywords: time integration; summation parts; class stable; integration ... See more keywords