An Approximation Theorist’s view on solving operator equations—With special attention to Trefftz, MFS, MPS, and DRM methods

When an Approximation Theorist looks at well-posed PDE problems or operator equations, and standard solution algorithms like Finite Elements, Rayleigh–Ritz or Trefftz techniques, methods of fundamental or particular solutions and their combinations, they boil down to approximation problems and stabi...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 88; pp. 70 - 77
Main Author Schaback, Robert
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 15.04.2021
Elsevier BV
Subjects
Algorithms
Approximation
Convergence
Discretization
Error analysis
Mathematical analysis
Meshless methods
Oversampling
Stability
Stability
Error analysis
Oversampling
Discretization
Meshless methods
Convergence
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Summary:When an Approximation Theorist looks at well-posed PDE problems or operator equations, and standard solution algorithms like Finite Elements, Rayleigh–Ritz or Trefftz techniques, methods of fundamental or particular solutions and their combinations, they boil down to approximation problems and stability issues. These two can be handled by Approximation Theory, and this paper shows how, with special applications to the aforementioned algorithms. The intention is that the Approximation Theorist’s viewpoint is helpful for readers who are somewhat away from that subject.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2019.09.005