- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:02
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
6
2004
2
Convergence for stabilisation of degenerately convex minimisation problems
S.
Bartels
Christian-Albrechts-Universität zu Kiel, KIEL, GERMANY
Carsten
Carstensen
Humboldt-Universität zu Berlin, BERLIN, GERMANY
P.
Plechac
University of Warwick, COVENTRY, UNITED KINGDOM
Andreas
Prohl
Universität Tübingen, TÜBINGEN, GERMANY
degenerate variational problems, convexification, stabilisation, strong convergence, Euler-Lagrange equations, calculus of variations
Degenerate variational problems often result from a relaxation technique in effective numerical simulation of nonconvex minimisation problems. The relaxed energy density is the convex envelope of the original one and so convex but not strictly convex. Hence strong convergence of straightforward finite element approximations cannot be expected but is relevant in many applications. This paper establishes a modified discretization by stabilisation and proves its convergence in strong norms.
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
253
269
10.4171/IFB/99
http://www.ems-ph.org/doi/10.4171/IFB/99