|
PSfile(gzip)
749Kb 874kb |
Charles M. Elliott, Yohei Kashima:A finite element analysis of critical state models for type-II superconductivity in 3DWe consider the numerical analysis of evolution variational inequalities which are derived from Maxwell's equations coupled with a nonlinear constitutive relation between the electric field and the current density and governing the magnetic field around a type-II bulk superconductor located in three dimensional space. The nonlinear Ohm's law is formulated using the sub-differential of a convex energy so the theory is applied to the Bean critical state model, a power law model and an extended Bean critical state model. The magnetic field in the nonconductive region is expressed as a gradient of a magnetic scalar potential in order to handle the curl free constraint. The variational inequalities are discretized in time implicitly and in space by Nedelec's curl conforming finite element of lowest order. The non-smooth energies are smoothed with a regularization parameter so that the fully discrete problem is a system of nonlinear algebraic equations at each time step. We prove various convergence results. Some numerical simulations under a uniform external magnetic field are presented.Bibliographical note: submitted to IMA journal of numerical analysis. |