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Flexible goal-oriented adaptivity for higher-order space–time discretizations of transport problems with coupled flow
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2020-09-18 , DOI: 10.1016/j.camwa.2020.08.028
Markus Bause , Marius Paul Bruchhäuser , Uwe Köcher

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.



中文翻译:

灵活的面向目标的适应性,用于耦合流下运输问题的高阶时空离散

在这项工作中,开发并研究了对流占主导的运输与耦合流体流动的灵活的高阶时空自适应有限元逼近。对流占主导地位的运输是多孔力学中一个具有挑战性的子问题,其中考虑了多孔介质中运输与流动,化学反应和机械反应的耦合。关键因素是双重加权残差(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,运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。误差估计允许时间和空间离散误差贡献的分离,这有助于同时调整时间和空间网格。

更新日期:2020-09-20
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