Convergence of the backward Euler method for type-II superconductors

Our paper is devoted to the study of a nonlinear degenerate transient eddy current problem of the type ∂t(|E|−1/pE)+∇×(∇×E)=0, p>1, along with appropriate initial and boundary conditions. We design a nonlinear time-discrete numerical scheme for the approximation in suitable function spaces. We show the well-posedness of the problem, prove the convergence of the approximation to a weak solution and finally derive the error estimates. In the proofs, the monotonicity methods and the Minty–Browder argument are employed.