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Moving mesh methods with upwinding schemes for time-dependent PDEs. (English) Zbl 0870.65076

A combination of moving meshes and upwinding schemes is considered for tracking the shock or steep wave front in the solution of partial differential equations. Several upwinding schemes are applied for uniform meshes. A self-adapting moving mesh method is also described. It is shown that the local piecewise hyperbolic method is very efficient and accurate when combined with a moving mesh strategy.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws

Software:

nag; DASSL
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Full Text: DOI Link

References:

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