High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes

• Published in: Computer methods in applied mechanics and engineering Vol. 342; pp. 414 - 437
• Main Authors: Antonietti, P.F., Mazzieri, I.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2018; Elsevier BV
• Subjects: Differential equations; Discontinuous Galerkin methods; Elastodynamics; Elastohydrodynamic lubrication; Finite element method; Galerkin method; Mathematical models; Numerical analysis; Polygonal and polyhedral grids; Propagation; Quadrilaterals; Wave propagation; 65M60; Discontinuous Galerkin methods; Wave propagation; Elastodynamics; 65M12; Polygonal and polyhedral grids
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2018.08.012

We propose and analyze a high-order Discontinuous Galerkin Finite Element Method for the approximate solution of wave propagation problems modeled by the elastodynamics equations on computational meshes made by polygonal and polyhedral elements. We analyze the well posedness of the resulting formulation, prove hp-version error a-priori estimates, and present a dispersion analysis, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion properties. The theoretical estimates are confirmed through various two-dimensional numerical verifications. •A new polygonal discontinuous Galerkin method is introduced for elastodynamics.•Stability and hp-version error estimates in a suitable energy norm are proved.•A dispersion analysis is carried out.•Dispersion errors are compared with those of classical spectral element methods.•The application of the method to benchmarks and realistic case studies is presented.