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In this paper, we use formal asymptotic arguments to understand the stability properties of equivariant solutions to the Landau–Lifshitz–Gilbert model for ferromagnets. We also analyse both the harmonic map heatflow and Schrödinger map flow limit cases. All asymptotic results are verified by detailed numerical experiments, as well as a robust topological argument. The key result of this paper is that blowup solutions to these problems are co-dimension one and hence both unstable and non-generic.

We derive a posteriori estimates for a discretization in space of the standardCahn–Hilliard equation with a double obstacle free energy.The derived estimates are robust and efficient, and in practice are combinedwith a heuristic time step adaptation. We present numerical experiments in two and three space dimensions and compareour method with an existing heuristic spatial mesh adaptation algorithm.

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(In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation

A posteriori estimates for the Cahn–Hilliard equationwith obstacle free energy

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2 results

(In-)stability of singular equivariant solutions to the Landau–Lifshitz–Gilbert equation

A posteriori estimates for the Cahn–Hilliard equationwith obstacle free energy