Ключевое слово: «continuous galerkin method»

This article provides a concise review of the Continuous Galerkin (CG) and Discontinuous Galerkin (DG) methods, focusing on their application for numerical simulation of elastic wave propagation in heterogeneous media. The study is based on a comparative analysis of these two finite element approaches. The CG method, which enforces solution continuity across element boundaries, is recognized for its efficiency in simulations involving smooth media and homogeneous materials. In contrast, the DG method, which allows for solution discontinuities and uses numerical fluxes for inter-element coupling, demonstrates superior flexibility and accuracy when modeling complex geological structures. Such structures include media with sharp material contrasts, layered formations, and fracture networks. The DG formulation naturally yields a block-diagonal mass matrix, facilitating efficient explicit time integration and enhanced parallel scalability. The review also underscores the critical role of selecting appropriate iterative solvers and preconditioners, such as Krylov subspace methods combined with algebraic multigrid or incomplete LU factorization, to optimize computational performance. The practical application of both methods is illustrated through numerical experiments simulating wave propagation in layered and fractured media, confirming the DG method's robustness for problems with internal discontinuities.