High-order schemes for Hamilton--Jacobi equations on triangular meshes
This paper concerns two weighted essentially nonoscillaotory (ENO) schemes on triangular meshes for Hamilton-Jacobi equations. Roughly speaking, weighted ENO schemes are central schemes in regions where the solution is smooth but emulate ENO schemes near the discontinuities of the solution. This is achieved by weighting the ENO substencils with weights adapted to the relative smoothness of the solution on these substencils. The two schemes with high-order accuracy, presented in this work, use the same set of triangular ENO stencils. One scheme uses a set of weights to recover the gradient of solution and has the same accuracy as ENO scheme. The other one uses different sets of weights to recover partial derivatives of solution and has high-order accuracy. Numerical examples are given.
weighted essentially nonoscillaotory schemes
scientific article; zbMATH DE number 2091379
scientific article