98 citations · 227 across the 32 of their papers we have counts for
45 papers
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…
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…
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…
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 topol…
Discretization error analysis for a radially symmetric harmonic map heat flow problem
Nam Anh Nguyen, Arnold Reusken
In this paper we study the harmonic map heat flow problem for a radially symmetric case. The corresponding partial dfferential equation plays a key role in many analyses of harmoni…
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…
A narrow band finite element method for the level set equation
Maxim Olshanskii, Arnold Reusken, Paul Schwering
A finite element method is introduced to track interface evolution governed by the level set equation. The method solves for the level set indicator function in a narrow band aroun…
Analysis of the Taylor-Hood Surface Finite Element Method for the surface Stokes equation
Arnold Reusken
We consider the surface Stokes equation on a smooth closed hypersurface in three-dimensional space. For discretization of this problem a generalization of the surface finite elemen…
Analysis of a space-time unfitted finite element method for PDEs on evolving surfaces
Arnold Reusken, Hauke Sass
In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order…
An Eulerian finite element method for tangential Navier-Stokes equations on evolving surfaces
Maxim A. Olshanskii, Arnold Reusken, Paul Schwering
The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth close…
An Accurate and Robust Eulerian Finite Element Method for Partial Differential Equations on Evolving Surfaces
Hauke Sass, Arnold Reusken
In this paper we present a new Eulerian finite element method for the discretization of scalar partial differential equations on evolving surfaces. In this method we use the restri…
Diffusion of tangential tensor fields: numerical issues and influence of geometric properties
Elena Bachini, Philip Brandner, Thomas Jankuhn +4
We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tange…
Tangential Navier-Stokes equations on evolving surfaces: Analysis and simulations
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
The paper considers a system of equations that models a lateral flow of a Boussinesq--Scriven fluid on a passively evolving surface embedded in . For the resulting Na…
Analysis of optimal preconditioners for CutFEM
Sven Gross, Arnold Reusken
In this paper we consider a class of unfitted finite element methods for scalar elliptic problems. These so-called CutFEM methods use standard finite element spaces on a fixed unfi…
On derivations of evolving surface Navier-Stokes equations
Philip Brandner, Arnold Reusken, Paul Schwering
In recent literature several derivations of incompressible Navier-Stokes type equations that model the dynamics of an evolving fluidic surface have been presented. These derivation…
Optimal preconditioners for a Nitsche stabilized fictitious domain finite element method
Sven Gross, Arnold Reusken
In this paper we consider a class of fictitious domain finite element methods known from the literature. These methods use standard finite element spaces on a fixed unfitted triang…
Finite element discretization methods for velocity-pressure and stream function formulations of surface Stokes equations
Philip Brandner, Thomas Jankuhn, Simon Praetorius +2
In this paper we study parametric TraceFEM and parametric SurfaceFEM (SFEM) discretizations of a surface Stokes problem. These methods are applied both to the Stokes problem in vel…
Analysis of finite element methods for surface vector-Laplace eigenproblems
Arnold Reusken
In this paper we study finite element discretizations of a surface vector-Laplace eigenproblem. We consider two known classes of finite element methods, namely one based on a vecto…
Analysis of the Schwarz domain decomposition method for the conductor-like screening continuum model
Arnold Reusken, Benjamin Stamm
We study the Schwarz overlapping domain decomposition method applied to the Poisson problem on a special family of domains, which by construction consist of a union of a large numb…
Error analysis of higher order trace finite element methods for the surface Stokes equations
Thomas Jankuhn, Maxim A. Olshanskii, Arnold Reusken +1
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood fini…
Finite Element Error Analysis of Surface Stokes Equations in Stream Function Formulation
Philip Brandner, Arnold Reusken
We consider a surface Stokes problem in stream function formulation on a simply connected oriented surface without boundary. This formulation leads to a cou…
Higher order Trace Finite Element Methods for the Surface Stokes Equation
Thomas Jankuhn, Arnold Reusken
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element ap…
Inf-sup stability of the trace P2-P1 Taylor-Hood elements for surface PDEs
Maxim A. Olshanskii, Arnold Reusken, Alexander Zhiliakov
The paper studies a geometrically unfitted finite element method (FEM), known as trace FEM or cut FEM, for the numerical solution of the Stokes system posed on a closed smooth surf…