An optimal order H1-Galerkin mixed finite element method for good Boussinesq equation

• Published in: Computational & applied mathematics Vol. 43; no. 7
• Main Authors: Doss, L. Jones Tarcius, Merlin, V. Jenish
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Boussinesq equations; Computational Mathematics and Numerical Analysis; Error analysis; Finite element method; Galerkin method; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Spline functions; 65M15; Mixed finite element method; Semi discrete and fully discrete scheme; Cubic B-spline; 35G20; Auxiliary projection; Good Boussinesq equation; Galerkin method; 65M60; 65N30; Optimal order error estimate
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-024-02914-0

In this paper, by introducing an intermediate function, a splitting technique is employed for the fourth order time dependent non-linear Good Boussinesq equation. Then, an H 1 -Galerkin mixed finite element method is applied to the Good Boussinesq (GB) equation with cubic spline space as test and trial space in the method. This method may be considered as a Petrov-Galerkin method in which cubic splines are trial and linear splines (i.e second derivative of cubic splines)as test space. Optimal order error estimates are obtained for the both semi discrete scheme and fully discrete scheme. The Numerical illustration is presented to support the theoretical analysis.