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A unified mixed finite element method for fourth-order time-dependent problems using biorthogonal systems.
- Source :
-
Computers & Mathematics with Applications . Jul2024, Vol. 165, p52-69. 18p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08981221
- Volume :
- 165
- Database :
- Academic Search Index
- Journal :
- Computers & Mathematics with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 177316374
- Full Text :
- https://doi.org/10.1016/j.camwa.2024.04.013