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Goal-oriented space-time adaptivity for the Navier--Stokes equations based on the dual weighted residual method
Marius Paul Bruchhäuser, Nils Margenberg, Markus Bause
This work presents a goal-oriented a posteriori error estimator based on the Dual Weighted Residual (DWR) method together with space-time mesh adaptivity for the Navier--Stokes equ…
Stochastic Galerkin and Monte-Carlo methods for parabolic problems: Numerical performance of variational matrix-free approximations
Moataz Dawor, Nils Margenberg, Markus Bause
Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational…
Solving the (Navier-)Stokes equations with space and time adaptivity using deal.II
Peter Munch, Marc Fehling, Martin Kronbichler +2
In this article, we solve the Stokes and Navier-Stokes equations with the dealII finite-element library. In particular, we use its multigrid, adaptive-mesh, and matrix-free infr…
A Scalable Monolithic Modified Newton Multigrid Framework for Time-Dependent -Navier-Stokes Flow
Nils Margenberg, Carolin Mehlmann
Fully implicit tensor-product space-time discretizations of time-dependent -Navier-Stokes models yield, on each time step, large nonlinear monolithic saddle-point systems. I…
Anisotropic hp space-time adaptivity and goal-oriented error control for convection-dominated problems
Nils Margenberg, Marius Paul Bruchhäuser, Bernhard Endtmayer
We present an anisotropic goal-oriented error estimator based on the Dual Weighted Residual (DWR) method for time-dependent convection-dominated problems. Using elementwise p-aniso…
A Monolithic hp Space-Time Multigrid Preconditioned Newton-Krylov Solver for Space-Time FEM applied to the Incompressible Navier-Stokes Equations
Nils Margenberg, Markus Bause
We present a monolithic hp space-time multigrid method (hp-STMG) for tensor-product space-time finite element discretizations of the incompressible Navier-Stokes equations. We empl…