Optimal convergence analysis of the virtual element methods for viscoelastic wave equations with variable coefficients on polygonal meshes

• Published in: BIT Vol. 64; no. 3
• Main Authors: Pradhan, Gouranga, Deka, Bhupen
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2024; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Convergence; Mathematical analysis; Mathematics; Mathematics and Statistics; Numeric Computing; Numerical analysis; Polygons; Viscoelasticity; Wave equations; 65N15; 65N12; Variable coefficients; Viscoelastic wave equations; Optimal convergence estimate; Virtual element method; 65N30
• ISSN: 0006-3835; 1572-9125
• DOI: 10.1007/s10543-024-01030-z

The objective of this work is to develop a conforming virtual element method for viscoelastic wave equations with variable coefficients on polygonal meshes. For problems where the coefficients are variable, the standard virtual element discrete forms do not work efficiently and require modification. For the optimal convergence estimate of the semi-discrete approximation in the L 2 norm, a special projection operator is used. In the fully discrete scheme, the implicit second-order Newmark method is employed to approximate the temporal derivatives. Numerical experiments are presented to support the theoretical results. The proposed numerical algorithm can be applied to various problems arising in the engineering and medical fields.