Solving partial differential equations on (evolving) surfaces with radial basis functions
| Autor: | Jens Künemund, Holger Wendland |
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| Rok vydání: | 2020 |
| Předmět: |
Partial differential equation
Collocation Discretization Applied Mathematics Significant part 010103 numerical & computational mathematics 01 natural sciences Mathematics::Numerical Analysis 010101 applied mathematics Computational Mathematics Kernel (image processing) Computer Science::Computational Engineering Finance and Science Applied mathematics Computational Science and Engineering Radial basis function 0101 mathematics Galerkin method Mathematics |
| Zdroj: | Advances in Computational Mathematics. 46 |
| ISSN: | 1572-9044 1019-7168 |
| DOI: | 10.1007/s10444-020-09803-0 |
| Popis: | Meshfree, kernel-based spatial discretisations are recent tools to discretise partial differential equations on surfaces. The goals of this paper are to analyse and compare three different meshfree kernel-based methods for the spatial discretisation of semi-linear parabolic partial differential equations (PDEs) on surfaces, i.e. on smooth, compact, connected, orientable, and closed (d − 1)-dimensional submanifolds of $\mathbb {R}^{d}$ . The three different methods are collocation, the Galerkin, and the RBF-FD method, respectively. Their advantages and drawbacks are discussed, and previously known theoretical results are extended and numerically verified. Finally, a significant part of this paper is devoted to solving PDEs on evolving surfaces with RBF-FD, which has not been done previously. |
| Databáze: | OpenAIRE |
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