String Gradient Weighted Moving Finite Elements in Multiple Dimensions with Applications in Two Dimensions

Wacher, Abigail; Sobey, Ian

doi:10.1137/040619557

String Gradient Weighted Moving Finite Elements in Multiple Dimensions with Applications in Two Dimensions

Wacher, Abigail; Sobey, Ian

Authors

Abigail Wacher

Ian Sobey

Abstract

We formulate the string gradient weighted moving finite element method (SGWMFE) for systems of PDEs in multiple dimensions. Then we illustrate implementation issues for the method using two dimensions. The method is applied successfully to solve the highly nonlinear unsteady porous medium equation in two dimensions and the results are compared to exact solutions. We proceed to present results for the method when applied to the Gray Scott chemical reaction diffusion model in two dimensions. Finally, we apply the method to the shallow water equations in two dimensions and compare the meshes produced with those produced using gradient weighted finite element methods (GWMFE). Our conclusion is that SGWMFE is an easily applied member of the group of moving finite element methods.

Citation

Wacher, A., & Sobey, I. (2007). String Gradient Weighted Moving Finite Elements in Multiple Dimensions with Applications in Two Dimensions. SIAM Journal on Scientific Computing, 29(2), 459-480. https://doi.org/10.1137/040619557

Journal Article Type	Article
Publication Date	Jan 1, 2007
Deposit Date	Jan 26, 2011
Publicly Available Date	Jan 28, 2011
Journal	SIAM Journal on Scientific Computing
Print ISSN	1064-8275
Electronic ISSN	1095-7197
Publisher	Society for Industrial and Applied Mathematics
Peer Reviewed	Peer Reviewed
Volume	29
Issue	2
Pages	459-480
DOI	https://doi.org/10.1137/040619557
Keywords	Moving finite elements, Mesh adaptation.