- Title
- A Mixed Finite Element Discretisation of Linear and Nonlinear Multivariate Splines Using the Laplacian Penalty Based on Biorthogonal Systems
- Creator
- Lamichhane, Bishnu P.
- Relation
- MethodsX Vol. 10, Issue 2023, no. 101962
- Publisher Link
- http://dx.doi.org/10.1016/j.mex.2022.101962
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2023
- Description
- We consider a mixed finite element method for a linear multivariate spline using the Laplacian penalty. Our discretisation is based on biorthogonal systems leading to a very simple and efficient finite element scheme. We also extend our approach to a nonlinear case and describe a split Bregman iteration scheme for the resulting nonlinear equations. We apply our numerical schemes to remove the mixture of Gaussian and impulsive noise for some test images. • This paper presents a method of discretising a multivariate spline using a finite element method.; • The method uses a biorthogonal system to achieve an efficient finite element method. ; • The method is extended to cover a discretisation scheme for a nonlinear case, including an adaptation of the split Bregman method for the nonlinear case.
- Subject
- multivariate spline; scattered data smoothing; mixed finite element method; biorthogonal system; total variation model; split Bregman method
- Identifier
- http://hdl.handle.net/1959.13/1479910
- Identifier
- uon:50409
- Identifier
- ISSN:2215-0161
- Rights
- © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0)
- Language
- eng
- Full Text
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