Gibbs Phenomena for L^q-Best Approximation in Finite Element Spaces -- Some Examples

09/02/2019 ∙ by Paul Houston, et al. ∙ 0

Recent developments in the context of minimum residual finite element methods are paving the way for designing finite element methods in non-standard function spaces. This, in particular, permits the selection of a solution space in which the best approximation of the solution has desirable properties. One of the biggest challenges in designing finite element methods are non-physical oscillations near thin layers and jump discontinuities. In this article we investigate Gibbs phenomena in the context of L^q-best approximation of discontinuities in finite element spaces with 1≤ q<∞. Using carefully selected examples, we show that on certain meshes the Gibbs phenomenon can be eliminated in the limit as q tends to 1. The aim here is to show the potential of L^1 as a solution space in connection with suitably designed meshes.



There are no comments yet.


page 29

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.