Publication

On nonlinear artificial viscosity, discrete maximum principle and hyperbolic conservation laws

Erik Burman
2007
Journal Articles

Abstract

A finite element method for Burgers' equation is studied. The method is analyzed using techniques from stabilized finite element methods and convergence to entropy solutions is proven under certain hypotheses on the artificial viscosity. In particular we assume that a discrete maximum principle holds. We then construct a nonlinear artificial viscosity that satisfies the assumptions required for convergence and that can be tuned to minimize artificial viscosity away from local extrema.

Official source

https://infoscience.epfl.ch/entities/publication/20cec5f0-9490-400f-87b2-8cd7c535780a

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Erik Burman
2007
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/20cec5f0-9490-400f-87b2-8cd7c535780a

About this result

Related concepts (19)

Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certain class (usually defined in terms of specified properties or measures), then the distribution with the largest entropy should be chosen as the least-informative default.

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In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

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