Details
| Original language | English |
|---|---|
| Pages (from-to) | 315-331 |
| Number of pages | 17 |
| Journal | Journal of Applied and Numerical Optimization |
| Volume | 3 |
| Issue number | 2 |
| Early online date | 23 Feb 2010 |
| Publication status | Published - 31 Aug 2021 |
Abstract
We analyze a finite element/boundary element procedure for a non-convex contact problem for the double–well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which may then be solved numerically. The convergence of the Galerkin approximations to certain macroscopic quantities and a corresponding a posteriori estimate for the approximation error are discussed. Numerical results illustrate the performance of the proposed method.
Keywords
- math.NA, math.AP, 65N38, 49M20, Interface problem, FE-BE coupling, Double–well potential
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
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In: Journal of Applied and Numerical Optimization, Vol. 3, No. 2, 31.08.2021, p. 315-331.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - FE-BE coupling for a transmission problem involving microstructure
AU - Gimperlein, Heiko
AU - Maischak, Matthias
AU - Schrohe, Elmar
AU - Stephan, Ernst P.
PY - 2021/8/31
Y1 - 2021/8/31
N2 - We analyze a finite element/boundary element procedure for a non-convex contact problem for the double–well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which may then be solved numerically. The convergence of the Galerkin approximations to certain macroscopic quantities and a corresponding a posteriori estimate for the approximation error are discussed. Numerical results illustrate the performance of the proposed method.
AB - We analyze a finite element/boundary element procedure for a non-convex contact problem for the double–well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which may then be solved numerically. The convergence of the Galerkin approximations to certain macroscopic quantities and a corresponding a posteriori estimate for the approximation error are discussed. Numerical results illustrate the performance of the proposed method.
KW - math.NA
KW - math.AP
KW - 65N38, 49M20
KW - Interface problem
KW - FE-BE coupling
KW - Double–well potential
UR - http://www.scopus.com/inward/record.url?scp=85105817722&partnerID=8YFLogxK
U2 - 10.23952/jano.3.2021.2.06
DO - 10.23952/jano.3.2021.2.06
M3 - Article
VL - 3
SP - 315
EP - 331
JO - Journal of Applied and Numerical Optimization
JF - Journal of Applied and Numerical Optimization
SN - 2562-5527
IS - 2
ER -