Log In Sign Up

Flexible goal-oriented space-time adaptivity for coupled Stokes flow and convection-dominated transport

by   Markus Bause, et al.

In this work, a flexible, fully space-time adaptive finite element approximation of a prototype multi-physics system coupling fluid flow and convection-dominated transport is developed and studied. By some minor generalization, the model becomes feasible for the simulation of a poroelasticity system. Automatic mesh adaptation is based on the Dual Weighted Residual method for goal-oriented a posteriori error estimation. In multi-physics, the reliable and economical computation of a specific functional, the so-called quantity of interest, is typically desirable. Here, adaptive algorithms become more involved since they need not only to control the time and space meshes, but also need to balance the contributions of the coupled subproblems to the error in the goal quantity. Key ingredients of the presented approach are the discontinuous Galerkin time discretization for the primal and dual problem of the DWR approach, permitting miscellaneous evaluations of the DWR error estimator, its implementation in an advanced software architecture and the separation of effects of temporal and spatial discretization which facilitates the simultaneous adjustment of the time and space mesh.


page 17

page 18

page 19


On the implementation of an adaptive multirate framework for coupled transport and flow

In this work, a multirate in time approach resolving the different time ...

Efficient and scalable data structures and algorithms for goal-oriented adaptivity of space-time FEM codes

The cost- and memory-efficient numerical simulation of coupled volume-ba...

A goal oriented error estimator and mesh adaptivity for sea ice simulations

For the first time we introduce an error estimator for the numerical app...

Space-Time-Parallel Poroelasticity Simulation

The accurate, reliable and efficient numerical approximation of multi-ph...

Where to Drill Next? A Dual-Weighted Approach to Adaptive Optimal Design of Groundwater Surveys

We present a novel approach to adaptive optimal design of groundwater su...