9 papers
An -adaptive strategy based on locally predicted error reductions
Patrick Bammer, Andreas Schröder, Thomas P. Wihler
We introduce a new -adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approa…
A numerical energy minimisation approach for semilinear diffusion-reaction boundary value problems based on steady state iterations
Mario Amrein, Pascal Heid, Thomas P. Wihler
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational sch…
Conditional a posteriori error bounds for high order DG time stepping approximations of semilinear heat models with blow-up
Stephen Metcalfe, Thomas P. Wihler
This work is concerned with the development of an adaptive numerical method for semilinear heat flow models featuring a general (possibly) nonlinear reaction term that may cause th…
Energy contraction and optimal convergence of adaptive iterative linearized finite element methods
Pascal Heid, Dirk Praetorius, Thomas P. Wihler
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Co…
Adaptive local minimax Galerkin methods for variational problems
Pascal Heid, Thomas P. Wihler
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are s…
Stability and Convergence of Spectral Mixed Discontinuous Galerkin Methods for 3D Linear Elasticity on Anisotropic Geometric Meshes
Thomas P. Wihler, Marcel Wirz
We consider spectral mixed discontinuous Galerkin finite element discretizations of the Lamé system of linear elasticity in polyhedral domains in . In order to resolv…