Convergence of higher order finite volume schemes on irregular grids |
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Authors: | Sebastian Noelle |
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Institution: | 1. Institute of Applied Mathematics, Bonn University, Wegeler St. 10, D-53115, Bonn, Germany
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Abstract: | We prove convergence to the entropy solution of a general class of higher order finite volume schemes on unstructured, irregular grids for multidimensional scalar conservation laws. Such grids allow for cells to become flat in the limit. We derive a new entropy inequality for higher order schemes built on Godunov’s numerical flux. Our result implies convergence of suitably modified versions of MUSCL-type finite volume schemes, ENO schemes and the discontinuous Galerkin finite element method. |
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