8 papers · 1 filter
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…
Adaptive iterative linearised finite element methods for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids
Pascal Heid, Endre Süli
In this work, we introduce an iterative linearised finite element method for the solution of Bingham fluid flow problems. The proposed algorithm has the favourable property that a…
On the convergence rate of the Kačanov scheme for shear-thinning fluids
Pascal Heid, Endre Süli
We explore the convergence rate of the Kačanov iteration scheme for different models of shear-thinning fluids, including Carreau and power-law type explicit quasi-Newtonian constit…
Gradient flow finite element discretisations with energy-based adaptivity for excited states of Schrödingers equation
Pascal Heid
We present an effective numerical procedure, which is based on the computational scheme from [Heid et al., arXiv:1906.06954], for the numerical approximation of excited states of S…
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…