Fully Discrete Scheme for Bean's Critical-state Model with Temperature Effects in Superconductivity

This paper considers a hyperbolic Maxwell variational inequality with temperature effects arising from Bean's critical-state model in type-II (high-temperature) superconductivity. Here, temperature...

[1]  R. Hiptmair.  Finite elements in computational electromagnetism , 2002, Acta Numerica.

[2]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[3]  C. P. Bean,et al.  Magnetization of High-Field Superconductors , 1964 .

[4]  Anna Nagurney,et al.  Variational Inequalities , 2009, Encyclopedia of Optimization.

[5]  Patrick Ciarlet,et al.  On the approximation of electromagnetic fields by edge finite elements. Part 1: Sharp interpolation results for low-regularity fields , 2016, Comput. Math. Appl..

[6]  John W. Barrett,et al.  A QUASI-VARIATIONAL INEQUALITY PROBLEM IN SUPERCONDUCTIVITY , 2010 .

[7]  C. Makridakis,et al.  Time-discrete finite element schemes for Maxwell's equations , 1995 .

[8]  C. P. Bean.  Magnetization of hard superconductors , 1962 .

[9]  I. Yousept.  Hyperbolic Maxwell variational inequalities of the second kind , 2020 .

[10]  Irwin Yousept,et al.  Optimal Control of Non-Smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity , 2017, SIAM J. Control. Optim..

[11]  Finite Element Analysis of a Current Density − Electric Field Formulation of Bean's Model for Superconductivity , 2005 .

[12]  F. Jochmann.  On a first-order hyperbolic system including Bean's model for superconductors with displacement current , 2009 .

[13]  I. Yousept.  Optimal control of quasilinear H(curl)-elliptic partial differential equations in magnetostatic field problems , 2013 .

[14]  A. Bossavit,et al.  Numerical modelling of superconductors in three dimensions: a model and a finite element method , 1994 .

[15]  A. Mukherjea,et al.  Real and Functional Analysis , 1978 .

[16]  Jean-Luc Guermond,et al.  Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions , 2017, Comput. Math. Appl..

[17]  V. Girault,et al.  Vector potentials in three-dimensional non-smooth domains , 1998 .

[18]  John W. Barrett,et al.  Sandpiles and superconductors: nonconforming linear finite element approximations for mixed formulations of quasi-variational inequalities , 2013 .

[19]  Jichun Li,et al.  Error analysis of fully discrete mixed finite element schemes for 3-D Maxwell’s equations in dispersive media , 2007 .

[20]  Ronald H. W. Hoppe,et al.  Finite element methods for Maxwell's equations , 2005, Math. Comput..

[21]  Leonid Prigozhin,et al.  Solution of Thin Film Magnetization Problems in Type-II Superconductivity , 1998 .

[22]  Haijun Wu,et al.  Edge Element Methods for Maxwell's Equations with Strong Convergence for Gauss' Laws , 2014, SIAM J. Numer. Anal..

[23]  Kazufumi Ito,et al.  Lagrange multiplier approach to variational problems and applications , 2008, Advances in design and control.

[24]  Jun Zou,et al.  Fully discrete finite element approaches for time-dependent Maxwell's equations , 1999, Numerische Mathematik.

[25]  Leonid Prigozhin,et al.  On the Bean critical-state model in superconductivity , 1996, European Journal of Applied Mathematics.

[26]  Jean-Luc Guermond,et al.  Finite element quasi-interpolation and best approximation , 2015, 1505.06931.

[27]  F. Kikuchi.  On a discrete compactness property for the Nedelec finite elements , 1989 .

[28]  Irwin Yousept.  Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity , 2017, SIAM J. Numer. Anal..

[29]  K. Müller,et al.  Origin of superconductive glassy state and extrinsic critical currents in high-Tc oxides. , 1987, Physical review letters.

[30]  Snorre H. Christiansen,et al.  Smoothed projections in finite element exterior calculus , 2007, Math. Comput..

[31]  Jun Zou,et al.  Edge Element Method for Optimal Control of Stationary Maxwell System with Gauss Law , 2017, SIAM J. Numer. Anal..

[32]  Charles M. Elliott,et al.  A Finite Element Approximation of a Variational Inequality Formulation of Bean's Model for Superconductivity , 2004, SIAM J. Numer. Anal..

[33]  Superconductivity modelling: homogenization of Bean's model in three dimensions, and the problem of transverse conductivity , 1995 .