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On the stability of meshless symmetric collocation for boundary value problems

journal contribution
posted on 2023-06-07, 23:25 authored by Holger Wendland
In this paper, we study the stability of symmetric collocation methods for boundary value problems using certain positive definite kernels. We derive lower bounds on the smallest eigenvalue of the associated collocation matrix in terms of the separation distance. Comparing these bounds to the well-known error estimates shows that another trade-off appears, which is significantly worse than the one known from classical interpolation. Finally, we show how this new trade-off can be overcome as well as how the collocation matrix can be stabilized by smoothing.

History

Publication status

  • Published

Journal

BIT Numerical Mathematics

ISSN

0006-3835

Publisher

Springer

Issue

2

Volume

47

Page range

455-468

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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