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Stefan Karch

Publications and source records attributed to Stefan Karch.

2 recordsLinked to original sources
arXiv2026

A posteriori error analysis for the second-order BDF method for the Landau-Lifshitz-Gilbert equation

The tangent plane scheme (TPS) is a well-established discretization of the Landau-Lifshitz-Gilbert (LLG) equation. However, rigorous a posteriori error estimates have not been established. In this work, we derive a rigorous a posteriori error estimate for the TPS based on the second-order backward differentiation formula (BDF(2)) in time and finite elements of arbitrary polynomial degree in space. The proposed estimators provide computable upper bounds for the temporal and spatial discretization errors on adaptive meshes with variable time-step sizes. This result establishes the mathematical foundation for fully adaptive algorithms for the LLG equation.

math.NA↗
arXiv2023

Adaptive mesh refinement for the Landau-Lifshitz-Gilbert equation

We propose a new adaptive algorithm for the approximation of the Landau-Lifshitz-Gilbert equation via a higher-order tangent plane scheme. We show that the adaptive approximation satisfies an energy inequality and demonstrate numerically, that the adaptive algorithm outperforms uniform approaches.

math.NA↗