We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modelling poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in space and time with inf-sup stable pairs of finite elements for the spatial approximation of the unknowns are investigated. Optimal order error estimates of energy-type are proven. Superconvergence at the time nodes is addressed briefly. The error analysis can be extended to discontinuous and enriched Galerkin space discretizations. The error estimates are confirmed by numerical experiments.
翻译:我们研究多物理学系统与超偏心电动与抛光迁移和模拟粒子和热弹性结合的时时定元素方法的数值近似值。这些方程式可及时改写为第一阶系统。用连续的Galerkin方法在空间和时间上与相向稳定成对的未知空间近似定元素进行分解。证明了对能源类型的最佳顺序误差估计。当节点处理时的超常相异性是简短的。错误分析可以扩展至不连续的和浓缩的Galerkin空间离散性。误差估计得到数字实验的证实。