Abstract
Abstract A robust finite element method is introduced for solving elastic vibration problems in two dimensions. The temporal discretization is carried out using the P 1 {P_{1}} -continuous discontinuous Galerkin (CDG) method, while the spatial discretization is based on the Crouziex–Raviart (CR) element. It is shown after a technical derivation that the error of the displacement (resp. velocity) in the energy norm (resp. L 2 {L^{2}} norm) is bounded by O ( h + k ) {O(h+k)} (resp. O ( h 2 + k ) {O(h^{2}+k)} ), where h and k denote the mesh sizes of the subdivisions in space and time, respectively. Under some regularity assumptions on the exact solution, the error bound is independent of the Lamé coefficients of the elastic material under discussion. A series of numerical results are offered to illustrate numerical performance of the proposed method and some other fully discrete methods for comparison.
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