Finite element methods for nonlinear elliptic and parabolic problems with memory properties | Zendy

Roger Van Keer | Zendy; Luc Dupré | Zendy

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Finite element methods for nonlinear elliptic and parabolic problems with memory properties

Author(s) -

Roger Van Keer,

Luc Dupré

Publication year - 1999

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1103149967

Subject(s) - finite element method , nonlinear system , mathematical analysis , mathematics , element (criminal law) , structural engineering , physics , engineering , political science , quantum mechanics , law

In this monograph we outline finite element methods for highly nonlinear boundary value problems of elliptic and parabolic type in 1D and 2D with memory effects. These problems arise e.g. from a recent topic in the mathematical theory of electromagnetism, viz the mathematical modelling and numerical evaluation of the electromagnetic field in magnetic materials showing hysteresis behaviour. Thus, in particular, we consider parabolic problems with nonlocal Neumann-BCs and we also consider the coupling of a transient 2D-problem with a vector hysteresis model. For each of the boundary value problems (BVPs) considered, the following 3 mathematical items are dealt with:

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