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Convergence of Semi-Lagrangian Approximations to Convex Hamilton-Jacobi Equations under (Very) Large Courant Numbers

Ferretti, Roberto

SIAM journal on numerical analysis, 2003-01, Vol.40 (6), p.2240-2253 [Periódico revisado por pares]

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Título:
Convergence of Semi-Lagrangian Approximations to Convex Hamilton-Jacobi Equations under (Very) Large Courant Numbers
Autor: Ferretti, Roberto
Assuntos: Approximation ; Conservation laws ; Exact sciences and technology ; Hamilton Jacobi equation ; Interpolation ; Logical givens ; Mathematical analysis ; Mathematical theorems ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Partial differential equations ; Partial differential equations, initial value problems and time-dependant initial-boundary value problems ; Perceptron convergence procedure ; Polynomials ; Sciences and techniques of general use ; Stencils
É parte de: SIAM journal on numerical analysis, 2003-01, Vol.40 (6), p.2240-2253
Descrição: We consider a class of semi-Lagrangian high-order approximation schemes for convex Hamilton-Jacobi equations. In this framework, we prove that under certain restrictions on the relationship between Δx and Δt, the sequence of approximate solutions is uniformly Lipschitz continuous and hence, by consistency, that it converges to the exact solution. The argument is suitable for most reconstructions of interest, including high-order polynomials and ENO reconstructions.
Editor: Philadelphia, PA: Society for Industrial and Applied Mathematics
Idioma: Inglês

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