A Finite Difference-Discontinuous Galerkin Method for the Wave Equation in Second Order Form

• We develop a hybrid spatial discretization for the wave equation in second order form, based on high-order accurate finite difference methods and discontinuous Galerkin methods. The hybridization combines computational efficiency of finite difference methods on Cartesian grids and geometrical flexibility of discontinuous Galerkin methods on unstructured meshes. The two spatial discretizations are coupled with a penalty technique at the interface such that the overall semidiscretization satisfies a discrete energy estimate to ensure stability. In addition, optimal convergence is obtained in the sense that when combining a fourth order finite difference method with a discontinuous Galerkin method using third order local polynomials, the overall convergence rate is fourth order. Furthermore, we use a novel approach to derive an error estimate for the semidiscretization by combining the energy method and the normal mode analysis for a corresponding one-dimensional model problem. The stability and accuracy analysis are verified in numerical experiments.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

finite difference methods

discontinuous Galerkin methods

hybrid methods

wave equations

normal mode analysis

Beräkningsvetenskap med inriktning mot numerisk analys

Scientific Computing with specialization in Numerical Analysis

Publication and Content Type

ref (subject category)

art (subject category)