- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
12
2010
1
A posteriori error controlled local resolution of evolving interfaces for generalized Cahn–Hilliard equations
Sören
Bartels
Universität Bonn, BONN, GERMANY
Rüdiger
Müller
Angewandte Analysis und Stochastik, BERLIN, GERMANY
For equations of generalized Cahn–Hilliard type we present an a posteriori error analysis that is robust with respect to a small interface length scale γ. We propose the solution of a fourth order elliptic eigenvalue problem in each time step to gain a fully computable error bound, which only depends polynomially (of low order) on the inverse of γ. A posteriori and a priori error bounds for the eigenvalue problem are also derived. In numerical examples we demonstrate that this approach extends the applicability of robust a posteriori error estimation as it removes restrictive conditions on the initial data. Moreover we show that the computation of the principal eigenvalue allows the detection of critical points during the time evolution that limit the validity of the estimate.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
45
74
10.4171/IFB/226
http://www.ems-ph.org/doi/10.4171/IFB/226