- Title
- A unified mixed finite element method for fourth-order time-dependent problems using biorthogonal systems
- Creator
- Das, Avijit; Lamichhane, Bishnu P.; Nataraj, Neela
- Relation
- Computers & Mathematics with Applications: an international Vol. 165, p. 52-69
- Publisher Link
- http://dx.doi.org/10.1016/j.camwa.2024.04.013
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2024
- Description
- This article introduces a unified mixed finite element framework based on a saddle-point formulation that applies to time-dependent fourth order linear and nonlinear problems with clamped, simply supported, and Cahn-Hilliard type boundary conditions. The classical mixed formulations lead to large matrix systems that demand huge storage and computational time making the schemes expensive, especially for the time-dependent problems. The proposed scheme circumvents this by employing biorthogonal basis functions that lead to sparse and positive-definite systems. The article discusses a mixed finite element method for the biharmonic problem and the time-dependent linear and nonlinear versions of the extended Fisher-Kolmogorov equations equipped with the aforementioned boundary conditions. The wellposedness of the scheme is discussed and a priori error estimates are presented for the semi-discrete and fully discrete finite element schemes. The numerical experiments validate the theoretical estimates derived in the paper.
- Subject
- extended Fisher-Kolmogorov problem; saddle point formulation; mixed finite elements; biorthogonal basis functions; error estimates
- Identifier
- http://hdl.handle.net/1959.13/1506291
- Identifier
- uon:55840
- Identifier
- ISSN:0898-1221
- Rights
- X
- Language
- eng
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