9 papers
Error analysis for a Finite Element Discretization of a corotational harmonic map heat flow problem
Nam Anh Nguyen, Arnold Reusken
We consider the harmonic map heat flow problem for a corotational case. For discretization of this problem we apply a -conforming finite element method in space combined with…
Well-posedness of the heat equation in domains with topological transitions
Maxim Olshanskii, Arnold Reusken
We analyze a linear parabolic equation with homogeneous Dirichlet boundary conditions posed in domains whose evolution may involve topological transitions. The domains are describe…
Numerical analysis of a constrained strain energy minimization problem
Tilman Aleman, Arnold Reusken
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information a…
Analysis of a finite element method for PDEs in evolving domains with topological changes
Maxim A. Olshanskii, Arnold Reusken
The paper presents the first rigorous error analysis of an unfitted finite element method for a linear parabolic problem posed on an evolving domain that may undergo a topo…
Analysis of a Schwarz-Fourier domain decomposition method
Arnold Reusken
The Schwarz domain decomposition method can be used for approximately solving a Laplace equation on a domain formed by the union of two overlapping discs. We consider an inexact va…
A comparative study of finite element methods for a class of harmonic map heat flow problems
Nam Anh Nguyen, Arnold Reusken
In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in to the uni…