×

zbMATH — the first resource for mathematics

Finite element solution of a nonlinear diffusion problem with a moving boundary. (English) Zbl 0605.65078
The above problem is a boundary-value problem simulating the redistribution of impurities in semiconductor device structures. The problem is formulated in a variational form. A fully discrete finite element solution is constructed. It is based on triangular elements varying in time. Stability of the scheme is proved and an error estimate derived. Some numerical results are introduced.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35R35 Free boundary problems for PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
78A55 Technical applications of optics and electromagnetic theory
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] 1 D J CHIN, M R KUMP and R W DUTTON, SUPRA-Stanford University Process Analysis Program, Stanford Electronics Laboratories Stanford University, Stanford, U S A , July 1981
[2] 2 T DUPONT, G FAIRWEATHER and J P Johnson, Three-Level Galerkin Methods for Parabolic Equations SIAM J Numer Anal 11 (1974), 392 410 Zbl0313.65107 MR403259 · Zbl 0313.65107 · doi:10.1137/0711034
[3] 3 M LEES, A priori Estimates for the Solutions of Difference Approximations to Parabolic Differential Equations Duke Math J 27 (1960), 287-311 Zbl0092.32803 MR121998 · Zbl 0092.32803 · doi:10.1215/S0012-7094-60-02727-7
[4] 4 C D MALDONADO, ROMANS II, A Two-Dimensional Process Simulator for Modeling and Simulation in the Design of VLSI Devices Applied Physics A31 (1983), 119-138
[5] 5 B R PENUMALLI, A Comprehensive Two-Dimensional VLSI Process Simulation Program BICEPS, IEEE Trans on Electron Devices 30 (1983), 986-992
[6] 6 M F WHEELER, A priori L 2 error estimates for Galerkin approximations to parabolic partial differential equations SIAM J Numer Anal 10 (1973), 723-759 Zbl0232.35060 MR351124 · Zbl 0232.35060 · doi:10.1137/0710062
[7] 7 M ZLAMAL, Curved Elements in the Finite Element Method I SIAM J Numer Anal 10 (1973), 229-240 Zbl0285.65067 MR395263 · Zbl 0285.65067 · doi:10.1137/0710022
[8] 8 M ZLAMAL, On the Finite Element Method Numer Math 12 (1968), 394-409 Zbl0176.16001 MR243753 · Zbl 0176.16001 · doi:10.1007/BF02161362 · eudml:131885
[9] 9 M ZLAMAL, Finite Element Methods for Nonlinear Parabolic Equations R A I R O Anal Numer 11 (1977), 93-107 Zbl0385.65049 MR502073 · Zbl 0385.65049 · eudml:193290
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.