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.

中文翻译：

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弹性振动问题的鲁棒有限元方法

摘要 介绍了一种求解二维弹性振动问题的鲁棒有限元方法。时间离散化使用 P 1 {P_{1}} - 连续不连续伽辽金 (CDG) 方法进行，而空间离散化基于 Crouziex-Raviart (CR) 元素。经技术推导可知，能量范数（即 L 2 {L^{2}} 范数）中位移（速度）的误差以 O ⁢ ( h + k ) {O(h +k)} (resp. O ⁢ ( h 2 + k ) {O(h^{2}+k)} )，其中 h 和 k 分别表示空间和时间细分的网格大小。在精确解的一些规律性假设下，误差界限与所讨论的弹性材料的拉梅系数无关。