Design and Application of a Gradient-Weighted Moving Finite Element Code II: in Two Dimensions

In part I the authors reported on the design of a robust and versatile gradient-weighted moving finite element (GWMFE) code in one dimension and on its application to a variety of PDEs and PDE systems. This companion paper does the same for the two-dimensional (2D) case. These moving node methods ar...

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Vydáno v:SIAM journal on scientific computing Ročník 19; číslo 3; s. 766 - 798
Hlavní autoři: Carlson, Neil N., Miller, Keith
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Society for Industrial and Applied Mathematics 01.05.1998
Témata:
Applied mathematics
Arsenic
Codes
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Semiconductors
Fluid mechanics
Program
Grid
Buckley Leverett equation
Variations
Moving finite element
Interpretation
Partial differential equation
Laplacian
Non linear model
Isotropic diffusion
Drift diffusion equation
Anisotropic scattering
Diffusion equation
Moving node
Regularization
ISSN:1064-8275, 1095-7197
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Shrnutí:In part I the authors reported on the design of a robust and versatile gradient-weighted moving finite element (GWMFE) code in one dimension and on its application to a variety of PDEs and PDE systems. This companion paper does the same for the two-dimensional (2D) case. These moving node methods are especially suited to problems which develop sharp moving fronts, especially problems where one needs to resolve the fine-scale structure of the fronts. The many potential pitfalls in the design of GWMFE codes and the special features of the implicit one-dimensional (1D) and 2D codes which contribute to their robustness and efficiency are discussed at length in part I; this paper concentrates on issues unique to the 2D case. Brief explanations are given of the variational interpretation of GWMFE, the geometrical-mechanical interpretation, simplified regularization terms, and the treatment of systems. A catalog of inner products which occur in GWMFE is given, with particular attention paid to those involving second-order operators. After presenting an example of the 2D phenomenon of grid collapse and discussing the need for long-time regularization, the paper reports on the application of the 2D code to several nontrivial problems---nonlinear arsenic diffusion in the manufacture of semiconductors, the drift-diffusion equations for semiconductor device simulation, the Buckley--Leverett black oil equations for reservoir simulation, and the motion of surfaces by mean curvature.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827594269561