3 papers
math.NA2019
Recurrent Neural Networks as Optimal Mesh Refinement Strategies
Jan Bohn, Michael Feischl
We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable param…
math.NA2019
Higher-order linearly implicit full discretization of the Landau--Lifshitz--Gilbert equation
Georgios Akrivis, Michael Feischl, Balázs Kovács +1
For the Landau--Lifshitz--Gilbert (LLG) equation of micromagnetics we study linearly implicit backward difference formula (BDF) time discretizations up to order combined with h…
math.AP2016
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
Michael Feischl, Thanh Tran
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initia…