Paper Info
Title
Robust A Priori and A Posteriori Error Analysis for the Approximation of Allen-Cahn and Ginzburg-Landau Equations Past Topological Changes
Abstract
A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the estimates in the presence of topological changes in the solution that represents singular points in the evolution. For typical singularities the estimates depend on the inverse of the parameter in a polynomial as opposed to exponential dependence of estimates resulting from a straightforward error analysis. The estimates naturally lead to adaptive mesh refinement and coarsening algorithms. Numerical experiments illustrate the reliability and efficiency of this approach for the evolution of interfaces and vortices that undergo topological changes.
Year
DOI
Venue
2011
10.1137/090751530
SIAM J. Numerical Analysis
Keywords
Field
DocType
mean curvature,robust a priori,. allen-cahn equation,ginzburg-landau equations past topological,posteriori error analysis,mesh refinement,particular attention,topological change,posteriori error estimate,numerical experiment,phase field model,coarsening algorithm,ginzburg-landau equation,numerical approximation,small parameter,straightforward error analysis,mean curvature flow,finite element method
Allen–Cahn equation,Topology,Mathematical optimization,Exponential function,Polynomial,Mathematical analysis,Scalar (physics),A priori and a posteriori,Adaptive mesh refinement,Gravitational singularity,Approximation error,Mathematics
Journal
Volume
Issue
ISSN
49
1
0036-1429
Citations 
PageRank 
References 
4
0.46
11
Authors
3
Name
Order
Citations
PageRank
Sören Bartels135556.90
Rüdiger Müller2202.71
Christoph Ortner37416.77