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Kernel-based discretisation for solving matrix-valued PDEs

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posted on 2023-06-09, 15:16 authored by Peter GieslPeter Giesl, Holger Wendland
In this paper, we discuss the numerical solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop and analyse a new meshfree discretisation scheme using kernel-based approximation spaces. However, since these pproximation spaces have now to be matrix-valued, the kernels we need to use are fourth order tensors. We will review and extend recent results on even more general reproducing kernel Hilbert spaces. We will then apply this general theory to solve a matrix-valued PDE and derive error estimates for the approximate solution. The paper ends with applications to typical examples from dynamical systems

History

Publication status

  • Published

File Version

  • Accepted version

Journal

SIAM Journal on Numerical Analysis

ISSN

0036-1429

Publisher

Society for Industrial and Applied Mathematics

Issue

6

Volume

56

Page range

3386-3406

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2018-09-28

First Open Access (FOA) Date

2018-09-28

First Compliant Deposit (FCD) Date

2018-09-27

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