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Finite element solution of the fundamental equations of semiconductor devices. II. (English) Zbl 1066.65107
The paper deals with a numerical approximation of an evolution nonlinear system of three semiconductor equations with constant mobilities. Mixed Dirichlet-Neumann boundary conditions are considered on a two-dimensional bounded domain. For the space discretization the standard linear triangular elements are used. The time discretization is done by means of an implicit finite difference scheme. This type of fully discrete approximation produces an unconditionally stable numerical scheme. Theorems on the existence and uniqueness of the discrete solution are proved under the minimum angle condition. The main theorem establishes the convergence in the \(C\)-norm of the proposed discrete solutions extended to the whole time interval as a piecewise linear functions. Part I of the paper has been published in Math. Comput. 46, 27–43 (1986; Zbl 0609.65089).
MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
82D37 Statistical mechanical studies of semiconductors
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References:
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