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math.NA2020
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…
math.NA2020
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…
math.NA2020
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…