A Lax-Wendroff type theorem for unstructured quasiuniform grids

Details A Lax-Wendroff type theorem for unstructured quasiuniform grids A Lax-Wendroff type theorem for unstructured quasiuniform grids

2005-09-14

arxiv.org/abs/math/0509331v1

Mathematics

Numerical Analysis

Scientific paper

A well-known theorem of Lax and Wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a.e. as the mesh parameter goes to zero, then the limit is a weak solution of the system. Moreover, if the scheme satisfies a discrete entropy inequality as well, the limit is an entropy solution. The original theorem applies to uniform Cartesian grids; this article presents a generalization for quasiuniform grids (with Lipschitz-boundary cells) uniformly continuous inhomogeneous numerical fluxes and nonlinear inhomogeneous sources. The added generality allows a discussion of novel applications like local time stepping, grids with moving vertices and conservative remapping. A counterexample demonstrates that the theorem is not valid for arbitrary non-quasiuniform grids.

Affiliated with

Also associated with

No associations

Rating

A Lax-Wendroff type theorem for unstructured quasiuniform grids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Lax-Wendroff type theorem for unstructured quasiuniform grids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Lax-Wendroff type theorem for unstructured quasiuniform grids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-407386