| Attributs | Valeurs |
|---|
| type
| |
| Is Part Of
| |
| Subject
| |
| License
| |
| Title
| - Gibbs phenomena for L q-best approximation in finite element spaces
|
| Date
| |
| has manifestation of work
| |
| related by
| |
| Author
| |
| Abstract
| - Recent developments in the context of minimum residual finite element methods are paving the way for designing quasi-optimal discretization methods in non-standard function spaces, such as q-type Sobolev spaces. For q → 1, these methods have demonstrated huge potential in avoiding the notorious Gibbs phenomena, i.e., the occurrence of spurious non-physical oscillations near thin layers and jump discontinuities. In this work we provide theoretical results that explain some of these numerical observations. In particular, we investigate the Gibbs phenomena for q-best approximations of discontinuities in finite element spaces with 1 ≤ q< ∞. We prove sufficient conditions on meshes in one and two dimensions such that over- and undershoots vanish in the limit q → 1. Moreover, we include examples of meshes such that Gibbs phenomena remain present even for q = 1 and demonstrate that our results can be used to design meshes so as to eliminate the Gibbs phenomenon.
|
| article type
| |
| publisher identifier
| |
| Date Copyrighted
| |
| Rights
| - © The authors. Published by EDP Sciences, SMAI 2022
|
| Rights Holder
| - The authors. Published by EDP Sciences, SMAI 2022
|
| is part of this journal
| |
| is primary topic
of | |
