A nonlinear relaxation formulation of the \(p\)-curl problem modelling high-temperature superconductors: a modified Yee's scheme

DOI10.1016/j.jcp.2018.11.027zbMath1416.78034OpenAlexW2901629409WikidataQ128901742 ScholiaQ128901742MaRDI QIDQ2314331

Yanyan Li

Publication date: 22 July 2019

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2018.11.027

zbMATH Keywords

Maxwell's equationsdegenerate parabolic equationhigh-temperature superconductorsnonlinear diffusionrelaxation schemeYee's scheme

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Electromagnetic theory (general) (78A25)

Uses Software

• COMSOL

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a \(p\)-curl system arising in electromagnetism
• Regularity of weak solution to a \(p\) -curl-system.
• Guaranteed and robust a posteriori error estimates and balancing discretization and linearization errors for monotone nonlinear problems
• Relaxation model for the \(p\)-Laplacian problem with stiffness
• A robust linearization scheme for nonlinear diffusion in type-II superconductors
• Fully discrete linear approximation scheme for electric field diffusion in type-II superconductors
• Diffusion limit of a hyperbolic system with relaxation
• The \(\nabla \cdot B=0\) constraint in shock-capturing magnetohydrodynamics codes
• Bean's critical-state model as the \(p\rightarrow\infty\) limit of an evolutionary \(p\)-Laplacian equation
• A degenerate evolution system modeling Bean's critical-state type-II superconductors
• Relaxation schemes for partial differential equations and applications to degenerate diffusion problems
• Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
• Convergence of the backward Euler method for type-II superconductors
• A Hierarchy of Models for Type-II Superconductors
• A posteriori FE error control for p-Laplacian by gradient recovery in quasi-norm
• High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems
• Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
• Numerical Passage from Systems of Conservation Laws to Hamilton--Jacobi Equations, and Relaxation Schemes
• A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations
• Finite Element Approximation of the Parabolic p-Laplacian
• Hyperbolic conservation laws with stiff relaxation terms and entropy
• On a 𝑝-Laplacian type of evolution system and applications to the Bean model in the type-II superconductivity theory
• Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation
• Existence and approximation of a mixed formulation for thin film magnetization problems in superconductivity

This page was built for publication: A nonlinear relaxation formulation of the \(p\)-curl problem modelling high-temperature superconductors: a modified Yee's scheme