论文标题
连续的Galerkin方法的融合，用于双曲 - 促羟基蛋白酶系统
Convergence of a continuous Galerkin method for hyperbolic-parabolic systems
论文作者
论文摘要
我们研究了多物理系统的时空有限元方法的数值近似，将双曲线弹性动力学与抛物线交通和抛物线型和热弹性建模。该方程在及时被重写为一阶系统。通过时间和空间变量的INF-SUP稳定对稳定对稳定对通过连续的Galerkin方法的离散化。最佳订单误差估计是通过描述系统未知数能量的加权规范的分析来证明的。分析的另一个重要成分和挑战是控制耦合术语。这里开发的技术可以推广到其他盖尔金空间离散和高级模型的家族。通过数值实验证实了误差估计值，也用于时间和空间中的高阶分段多项式。后者导致具有复杂块结构的代数系统，并在迭代求解器的设计上构成了挑战的方面。参考有效的解决方案技术。
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a first-order system in time. Discretizations by continuous Galerkin methods in time and inf-sup stable pairs of finite element spaces for the spatial variables are investigated. Optimal order error estimates are proved by an analysis in weighted norms that depict the energy of the system's unknowns. A further important ingredient and challenge of the analysis is the control of the couplings terms. The techniques developed here can be generalized to other families of Galerkin space discretizations and advanced models. The error estimates are confirmed by numerical experiments, also for higher order piecewise polynomials in time and space. The latter lead to algebraic systems with complex block structure and put a facet of challenge on the design of iterative solvers. An efficient solution technique is referenced.
