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Journal of Scientific Computing

Erschienen in:

03.07.2015

A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems

verfasst von: Bishnu P. Lamichhane, Stephen G. Roberts, Linda Stals

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2016

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Abstract

The thin plate spline method is a widely used data fitting technique as it has the ability to smooth noisy data. Here we consider a mixed finite element discretisation of the thin plate spline. By using mixed finite elements the formulation can be defined in-terms of relatively simple stencils, thus resulting in a system that is sparse and whose size only depends linearly on the number of finite element nodes. The mixed formulation is obtained by introducing the gradient of the corresponding function as an additional unknown. The novel approach taken in this paper is to work with a pair of bases for the gradient and the Lagrange multiplier forming a biorthogonal system thus ensuring that the scheme is numerically efficient, and the formulation is stable. Some numerical results are presented to demonstrate the performance of our approach. A preconditioned conjugate gradient method is an efficient solver for the arising linear system of equations.

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Titel: A Mixed Finite Element Discretisation of Thin Plate Splines Based on Biorthogonal Systems
verfasst von: Bishnu P. Lamichhane
Stephen G. Roberts
Linda Stals
Publikationsdatum: 03.07.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0068-6

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