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A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations

Abigail Wacher (2013)

Open Mathematics

We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium equation, both...

A quasi-variational inequality problem arising in the modeling of growing sandpiles

John W. Barrett, Leonid Prigozhin (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Existence of a solution to the quasi-variational inequality problem arising in a model for sand surface evolution has been an open problem for a long time. Another long-standing open problem concerns determining the dual variable, the flux of sand pouring down the evolving sand surface, which is also of practical interest in a variety of applications of this model. Previously, these problems were solved for the special case in which the inequality is simply variational. Here, we introduce a regularized...

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