A stabilised mixed finite element method for thin plate splines based on biorthogonal systems

Authors

  • Bishnu Prasad Lamichhane
  • Markus Hegland Centre for Mathematics and its Applications, Mathematical Sciences Institute Australian National University, Canberra, ACT 0200, Australia.

DOI:

https://doi.org/10.21914/anziamj.v54i0.6218

Keywords:

Thin plate splines, scattered data smoothing, mixed finite element method, saddle point problem, biorthogonal system, a priori estimate

Abstract

We propose a novel stabilised mixed finite element method for the discretisation of thin plate splines. The mixed formulation is obtained by introducing the gradient of the smoother as an additional unknown. Working with a pair of bases for the gradient of the smoother and the Lagrange multiplier, which forms a biorthogonal system, we eliminate these two variables (gradient of the smoother and Lagrange multiplier) leading to a positive definite formulation. We prove a sub-optimal a priori error estimate for the proposed finite element scheme. References
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Author Biographies

Bishnu Prasad Lamichhane

Lecturer at the university of Newcastle

Markus Hegland, Centre for Mathematics and its Applications, Mathematical Sciences Institute Australian National University, Canberra, ACT 0200, Australia.

Professor at the Australian National University

Published

2013-05-12

Issue

Section

Proceedings Computational Techniques and Applications Conference