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\(r\)-refinement for evolutionary PDEs with finite elements or finite differences. (English) Zbl 0891.65101

The author establishes the main differences and similarities with respect to the grid properties of two methods from the class of \(r\)-refinements methods, namely, moving finite elements and moving finite differences. The usefulness of \(r\)-refinement, even in 1D, is shown by considering a reaction-diffusion system for two irreversible chemical reactions. The effect of collapsing grids in 2D is considered in connection with a first-order hyperbolic partial differential equation.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
92E20 Classical flows, reactions, etc. in chemistry
35K57 Reaction-diffusion equations
80A32 Chemically reacting flows
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems

Software:

DASSL; NKA
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Full Text: DOI

References:

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