122 citations · 152 across the 15 of their papers we have counts for
16 papers
A collocation scheme that is equivalent to discontinuous Galerkin discretizations
Jason Hicken
A spectral collocation operator with the summation-by-parts property was introduced by Chan to develop entropy-stable discontinuous Galerkin (DG) semi-discretizations (https://doi.…
Very high-order symmetric positive-interior quadrature rules on triangles and tetrahedra
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present novel fully-symmetric quadrature rules with positive weights and strictly interior nodes of degrees up to 84 on triangles and 40 on tetrahedra. Initial guesses for solvi…
Constructing stable, high-order finite-difference operators on point clouds over complex geometries
Jason Hicken, Ge Yan, Sharanjeet Kaur
High-order difference operators with the summation-by-parts (SBP) property can be used to build stable discretizations of hyperbolic conservation laws; however, most high-order SBP…
Tensor-Product Split-Simplex Summation-By-Parts Operators
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
We present an approach to construct efficient sparse summation-by-parts (SBP) operators on triangles and tetrahedra with a tensor-product structure. The operators are constructed b…
Quadrature Rules on Triangles and Tetrahedra for Multidimensional Summation-By-Parts Operators
Zelalem Arega Worku, Jason E. Hicken, David W. Zingg
Multidimensional diagonal-norm summation-by-parts (SBP) operators with collocated volume and facet nodes, known as diagonal- operators, are attractive for entropy-sta…
Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws
Ge Yan, Sharanjeet Kaur, Jeffery W. Banks +1
The paper describes the construction of entropy-stable discontinuous Galerkin difference (DGD) discretizations for hyperbolic conservation laws on unstructured grids. The construct…