Hyperbolic Maxwell Variational Inequalities for Bean's Critical-State Model in Type-II Superconductivity

DOI10.1137/16M1091939zbMath1377.35201MaRDI QIDQ5372081

Irwin Yousept

Publication date: 24 October 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

convergence analysiserror analysismixed finite elementRitz-Galerkin approximation

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Maxwell equations (35Q61) Unilateral problems for hyperbolic systems and systems of variational inequalities with hyperbolic operators (35L87)

Related Items

Strong Stationarity for Optimal Control of Variational Inequalities of the Second Kind, Maxwell Variational Inequalities in Type-II Superconductivity, Maxwell quasi-variational inequalities in superconductivity, Eddy current approximation in Maxwell obstacle problems, Quasilinear Variational Inequalities in Ferromagnetic Shielding: Well-Posedness, Regularity, and Optimal Control, Hyperbolic Maxwell variational inequalities of the second kind, Optimal control of elliptic variational inequalities with bounded and unbounded operators, Adaptive Edge Element Approximation for H(curl) Elliptic Variational Inequalities of Second Kind, Variational source condition for ill-posed backward nonlinear Maxwell’s equations, Well-posedness theory for electromagnetic obstacle problems, Shape Optimization for Superconductors Governed by H(curl)-Elliptic Variational Inequalities, Fully Discrete Scheme for Bean's Critical-state Model with Temperature Effects in Superconductivity, Numerical Analysis for Maxwell Obstacle Problems in Electric Shielding

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal control of Maxwell's equations with regularized state constraints
• A variational inequality in Bean's model for superconductors with displacement current
• Dual formulations in critical state problems
• On a first-order hyperbolic system including Bean's model for superconductors with displacement current
• Eddy current approximation of Maxwell equations. Theory, algorithms and applications
• Well-posedness for Bean's critical state model with displacement current
• Mixed finite elements in \(\mathbb{R}^3\)
• The Bean model in superconductivity: Variational formulation and numerical solution
• A Hierarchy of Models for Type-II Superconductors
• Optimal Control of Quasilinear $\boldsymbol{H}(\mathbf{curl})$-Elliptic Partial Differential Equations in Magnetostatic Field Problems
• Magnetization of Hard Superconductors
• Finite elements in computational electromagnetism
• A finite-element analysis of critical-state models for type-II superconductivity in 3D
• Finite Element Methods for Navier-Stokes Equations
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Vector potentials in three-dimensional non-smooth domains
• On a non‐stationary Ginzburg–Landau superconductivity model
• A Finite Element Approximation of a Variational Inequality Formulation of Bean's Model for Superconductivity
• Finite Element Methods for Maxwell's Equations
• Time-discrete finite element schemes for Maxwell's equations
• Sandpiles and superconductors: nonconforming linear finite element approximations for mixed formulations of quasi-variational inequalities
• Optimal Control of Non-Smooth Hyperbolic Evolution Maxwell Equations in Type-II Superconductivity
• Existence and approximation of a mixed formulation for thin film magnetization problems in superconductivity