A Staggered Discontinuous Galerkin Method for the Simulation of Wave Propagation in Poroelastic Media

• Published in: Journal of computational methods in applied mathematics Vol. 25; no. 3; pp. 741 - 757
• Main Author: Zhao, Lina
• Format: Journal Article
• Language: English
• Published: Minsk De Gruyter 01.07.2025; Walter de Gruyter GmbH
• Subjects: 65M12; 65M15; 65M22; Convergence; DG Method; Galerkin method; Lagrange multiplier; Polygonal Meshes; Polygons; Poroelastic Media; Poroelasticity; Staggered Grid; Wave Propagation
• ISSN: 1609-4840; 1609-9389
• DOI: 10.1515/cmam-2024-0194

In this paper, we design a staggered discontinuous Galerkin method for the wave propagation in poroelastic media on general polygonal meshes. The proposed method is robust with respect to the shape of the grids and can handle hanging nodes simply. The scheme shows great advantage in handling problems with complex geometries. The scheme is constructed based on the first-order hyperbolic velocity-stress system of the governing equations (i.e., Biot’s equations). Staggered continuities are imposed for the construction of the approximation spaces, as such penalty term is not needed in contrast to other DG methods. The symmetry of stress is weakly enforced via the introduction of a suitable Lagrange multiplier. The stability and convergence error estimates are analyzed. Several numerical experiments are carried out to test the performances of the proposed scheme. Numerical experiments confirm that the proposed scheme can handle polygonal elements with arbitrarily small edges without losing convergence order.