Convergence of the backward Euler method for type-II superconductors |
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Authors: | Marián Slodi?ka |
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Institution: | Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, B-9000 Gent, Belgium |
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Abstract: | 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. |
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Keywords: | Superconductors Nonlinear degenerate eddy current problem Time discretization Minty-Browder |
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