Gibbs phenomena for L<i><sup>q</sup></i>-best approximation in finite element spaces
نویسندگان
چکیده
Recent developments in the context of minimum residual finite element methods are paving way for designing quasi-optimal discretization non-standard function spaces, such as q -type Sobolev spaces. For ? 1, these have demonstrated huge potential avoiding notorious Gibbs phenomena, i.e. , occurrence spurious non-physical oscillations near thin layers and jump discontinuities. In this work we provide theoretical results that explain some numerical observations. particular, investigate phenomena -best approximations discontinuities spaces with 1 ? < ?. We prove sufficient conditions on meshes one two dimensions over- undershoots vanish limit 1. Moreover, include examples remain present even = demonstrate our can be used to design so eliminate phenomenon.
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ژورنال
عنوان ژورنال: ESAIM
سال: 2022
ISSN: ['1270-900X']
DOI: https://doi.org/10.1051/m2an/2021086