Linear Scheme for Finite Element Solution of Nonlinear Parabolic-Elliptic Problems with Nonhomogeneous Dirichlet Boundary Condition

The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part Γ^sub 1^ of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand side by the explicit Euler method). The scheme we get is linear. The strong convergence of the method is proved under the assumptions that the boundary [partial differential]Ω is piecewise of class C^sup 3^ and the initial condition belongs to L^sub 2^ only. Strong monotonicity and Lipschitz continuity of the form a(v,w) is not an assumption, but a property of this form following from its physical background.[PUBLICATION ABSTRACT]