A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation

Authors

Samir Karaa, Department of Mathematics and Statistics, College of Science, Sultan Qaboos University, P.O. Box: 36, Al-Khod 123, Muscat, Sultanate of Oman.

Abstract

A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method employs a three-level one-parameter scheme. A rigorous stability analysis is presented based on energy estimation and sharp stability results are obtained. A convergence analysis is carried out and optimal a priorierror estimates for both displacement and pressure are derived.

Recommended Citation

Karaa, Samir (2015) A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation, Sultan Qaboos University Journal For Science: Vol. 20: Iss. 2, 31-41.
DOI: https://doi.org/10.24200/squjs.vol20iss2pp31-41
Available at: https://squjs.squ.edu.om/squjs/vol20/iss2/5