On Families of Pointwise Optimal Finite Volume ENO Approximations

Authors:
Thomas Sonar
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
1998

Citing 0
Cited 4

Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation

Journal of Computational Physics
From continuous recovery to discrete filtering in numerical approximations of conservation laws

Applied Numerical Mathematics
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions

Journal of Computational Physics
Limiting strategies for polynomial reconstructions in the finite volume approximation of the linear advection equation

Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization

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Abstract

The present work is devoted to the construction of radial functions which can serve as recovery functions in essentially nonoscillatory (ENO) approximations of hyperbolic conservation laws on unstructured grids. Conditionally positive $\lambda$-definite radial functions are shown to be pointwise optimal and therefore very well suited for use in finite volume schemes. In the present paper we develop the theory of pointwise optimality and give examples.