Verdi, C.; Visintin, A. Numerical approximation of the Preisach model for hysteresis. (English) Zbl 0672.65115 RAIRO, Modélisation Math. Anal. Numér. 23, No. 2, 335-356 (1989). The authors define a continuous hysteresis operator \(F_{\mu}\), which has a natural geometrical interpretation. They then consider the equation \(\partial /\partial t[u+F_{\mu}(u)]-\nabla^ 2u=f\) and indicate how it and a corresponding integral equation can be solved numerically by discretization techniques. A Fortran based implementation of the approximation for \(F_{\mu}\) is included. Reviewer: Ll.G.Chambers Cited in 4 Documents MSC: 65R20 Numerical methods for integral equations 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 78A30 Electro- and magnetostatics Keywords:Preisach model; initial and boundary value problem; weak solution; finite element space approximations; time discretizations; backward; differences; linearization; stability; Fortran implementation; continuous hysteresis operator PDFBibTeX XMLCite \textit{C. Verdi} and \textit{A. Visintin}, RAIRO, Modélisation Math. Anal. Numér. 23, No. 2, 335--356 (1989; Zbl 0672.65115) Full Text: DOI EuDML References: [1] M. BROKATE & A. VISINTIN, Properties of the Preisach model for hysteresis, Preprint (1988). Zbl0682.47034 MR1022792 · Zbl 0682.47034 · doi:10.1515/crll.1989.402.1 [2] P. G. CIARLET, The finite element method for elliptic problems, North-Holland, Amsterdam (1978). Zbl0383.65058 MR520174 · Zbl 0383.65058 [3] K.-H. HOFFMANN, J. SPREKELS & A. VISINTIN, Identification of hysteresis loops, J. Comp. Phys., 78 (1988), 215-230. Zbl0659.65125 MR959083 · Zbl 0659.65125 · doi:10.1016/0021-9991(88)90045-9 [4] M. A. KRASNOSEL SKII & A. V. POKROVSKII, Systems with hysteresis (Russian), Nauka, Moscow (1983), English translation, Springer-Verlag, Berlin (1989). Zbl0665.47038 MR987431 · Zbl 0665.47038 [5] [5] E. MAGENES, R. H. NOCHETTO & C. VERDI, Energy error estimates for a linear scheme to approximate nonlinear parabolic problems, RAIRO Model Math. Anal. Numer., 21 (1987), 655-678. Zbl0635.65123 MR921832 · Zbl 0635.65123 [6] J. M. ORTEGA & C. RHEIBOLDT, Iterative solution of non-linear equations in several variables, Academic Press, New York (1970). Zbl0241.65046 · Zbl 0241.65046 [7] E. PREISACH, Uber die magnetische Nachwirkung, Z. Phisik, 94 (1935), 277-302. [8] C. VERDI & A. VISINTIN, Numerical approximation of hysteresis problems, I M A J Numer Anal, 5 (1985), 447-463. Zbl0608.65082 MR816068 · Zbl 0608.65082 · doi:10.1093/imanum/5.4.447 [9] [9] C. VERDI & A. VISINTIN, Error estimates for a semi-explicit numerical scheme for Stefan-type problems, Numer. Math., 52 (1988), 165-185. Zbl0617.65125 MR923709 · Zbl 0617.65125 · doi:10.1007/BF01398688 [10] A. VISINTIN, On the Preisach model for hysteresis, Non linear Anal, 9 (1984), 977-996. Zbl0563.35007 MR760191 · Zbl 0563.35007 · doi:10.1016/0362-546X(84)90094-4 [11] A. VISINTIN, Mathematical models of hysteresis, in Topics in Nonsmooth Analysis (J. J. Moreau, P. D. Panagiotopoulos & G Strang, Eds ), Birkhauser, Basel (1988). Zbl0656.73043 MR957094 · Zbl 0656.73043 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.