论文标题
柔性目标适应性，用于耦合流量的高阶时空离散
Flexible goal-oriented adaptivity for higher-order space-time discretizations of transport problems with coupled flow
论文作者
论文摘要
在这项工作中，开发和研究了对流为主的传输的灵活高阶时空自适应有限元近似。以对流为主的运输是一种具有挑战性的门能子问题，其中考虑了多孔培养基中的流量，化学反应和机械响应的耦合传输。关键成分是双重加权残差方法（DWR）方法的原始问题和双重问题的任意程度不连续的Galerkin时间离散化，这是对传输问题的后验误差估计，以及流量及其在高级软件体系结构中的实现。误差估算允许分离时间和空间离散误差贡献，从而有助于同时调整时间和空间网格。该方法的性能及其软件实施是通过数值收敛示例研究的，也是对流为主案例的身体兴趣的示例。
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in poromechanics in which coupled transport with flow, chemical reaction and mechanical response in porous media is considered. Key ingredients are the arbitrary degree discontinuous Galerkin time discretization of the primal and dual problems for the Dual Weighted Residual (DWR) approach, an a posteriori error estimation for the transport problem coupled with flow and its implementation in an advanced software architecture. The error estimate allows the separation of the temporal and spatial discretization error contributions which facilitates the simultaneous adjustment of the time and space mesh. The performance of the approach and its software implementation is studied by numerical convergence examples as well as an example of physical interest for convection-dominated cases.
