Jan Philipp Thiele's research while affiliated with Leibniz Universität Hannover and other places

Publications (6)

Preprint
Full-text available
In this work, the dual-weighted residual method is applied to a space-time formulation of nonstationary Stokes and Navier-Stokes flow. Tensor-product space-time finite elements are being used to discretize the variational formulation with discontinuous Galerkin finite elements in time and inf-sup stable Taylor-Hood finite element pairs in space. To...
Preprint
Full-text available
In this work, we consider space-time goal-oriented a posteriori error estimation for parabolic problems. Temporal and spatial discretizations are based on Galerkin finite elements of continuous and discontinuous type. The main objectives are the development and analysis of space-time estimators, in which the localization is based on a weak form emp...
Preprint
Full-text available
In this work, a space-time scheme for goal-oriented a posteriori error estimation is proposed. The error estimator is evaluated using a partition-of-unity dual-weighted residual method. As application, a low mach number combustion equation is considered. In some numerical tests, different interpolation variants are investigated, while observing con...
Article
In this work, space-time goal-oriented a posteriori error estimation using a partition-of-unity localization is applied to the linear heat equation. The algorithmic developments are substantiated with a numerical example.
Chapter
In this work, we further develop multigoal-oriented a posteriori error estimation for the nonlinear, stationary, incompressible Navier-Stokes equations. It is an extension of our previous work on two-side a posteriori error estimates for the DWR method. We now focus on h enrichment and p enrichment for the error estimator. These advancements are de...
Preprint
In this work, we further develop multigoal-oriented a posteriori error estimation for the nonlinear, stationary, incompressible Navier-Stokes equations. It is an extension of our previous work [B. Endtmayer, U. Langer, T. Wick: Two-side a posteriori error estimates for the DWR method, $SISC$, 2019, accepted]. We now focus on $h$ mesh refinement and...

Citations

... We will, however, limit ourselves to the variation of finite element orders in space and use the equal order approach for the temporal discretization. We also notice that some preliminary results on space-time adaptivity with the PU-DWR method are published in [15]. ...
... • continuous piecewise bi-quartic functions Q c 4 for the velocity v and • continuous piecewise quadratic functions Q c 2 for the pressure p and temperature ϑ. A comparison of different finite elements and uniform mesh refinement for the enriched space can be found in [59]. ...