A linear scheme for the numerical solution of nonlinear quasistationary magnetic fields
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- by Miloš Zlámal PDF
- Math. Comp. 41 (1983), 425-440 Request permission
Abstract:
The computation of nonlinear quasistationary two-dimensional magnetic fields leads to the following problem. There exists a bounded domain $\Omega$ and an open nonempty set $R \subset \Omega$. We are looking for the magnetic vector potential $u({x_1},{x_2},t)$ which satisfies: (1) a certain nonlinear parabolic equation and an initial condition in R, (2) a nonlinear elliptic equation in $S = \Omega - \bar R$, (3) a boundary conditon on $\partial \Omega$ and the condition that u as well as its conormal derivative are continuous across $\Gamma = \partial R \cap \partial S$. This problem is formulated in an abstract variational way. We construct an approximate solution discretized in space by a generalized Galerkin method and by a one-step method in time. The resulting scheme is unconditionally stable and linear. A strong convergence of the approximate solution is proved without any regularity assumptions for the exact solution. We also derive an error bound for the solution of the two-dimensional magnetic field equations under the assumption that the exact solution is sufficiently smooth.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 41 (1983), 425-440
- MSC: Primary 65N30; Secondary 78-08, 78A30
- DOI: https://doi.org/10.1090/S0025-5718-1983-0717694-1
- MathSciNet review: 717694