paper_siam_revision_accepted.pdf (1.71 MB)
Kernel-based discretisation for solving matrix-valued PDEs
journal contribution
posted on 2023-06-09, 15:16 authored by Peter GieslPeter Giesl, Holger WendlandIn 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 AnalysisISSN
0036-1429Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
6Volume
56Page range
3386-3406Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes