论文信息 - Comment on "A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions"

Comment on "A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions"

Abstract This comment concerns a mistake in the proving of positivity-preserving property for the well-balanced discontinuous Galerkin methods presented by Meister and Ortleb [Meister A, Ortleb S, A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions, Applied Mathematics and Computation 272 (2016) 259–273]. Furthermore, we provide a correct proof which gives the same result.

Longxiang Li | Qinghe Zhang

[1] G. Petrova,et al. A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ , 2007 .

[2] Andreas Meister,et al. A positivity preserving and well-balanced DG scheme using finite volume subcells in almost dry regions , 2016, Appl. Math. Comput..

[3] Yulong Xing,et al. Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes , 2013, J. Sci. Comput..