Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws

Authors:
Laurent Gosse;Charalambos Makridakis
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

Citing 0
Cited 3

An adaptive method with rigorous error control for the Hamilton-Jacobi equations: part I: The one-dimensional steady state case

Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Essentially Non-Oscillatory Adaptive Tree Methods

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An adaptive method with rigorous error control for the Hamilton--Jacobi equations. Part I: The one-dimensional steady state case

Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation

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Abstract

In this paper, we propose a posteriori local error estimates for numerical schemes in the context of one-dimensional scalar conservation laws. We first consider the schemes for which a consistent in-cell entropy inequality can be derived. Then we extend this result to second-order schemes written in viscous form satisfying weak entropy inequalities. As an illustration, we show several numerical tests on the Burgers equation and we propose an adaptive algorithm for the selection of the mesh.