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The finite element method is used to solve the non‐linear diffusion equation, taking account of the interaction between impurities due to self‐induced electric field and charged vacancies effects, and of various boundary conditions (evaporation, segregation, oxidation growth…). An incomplete implicit scheme gives the solution of the temporal equation deduced from a quadratic space discretization. The temporal and spatial problems being proved to be quite independent, specific locally refined meshes are developed. The quadratic shape functions allow the use of evolutive mesh for the oxidation simulation without profile degradation. Two realistic industrial steps are described to demonstrate the efficiency of the code.

This paper gives a bibliographical review of the finite element methods (FEMs) applied to the analysis of ceramics and glass materials. The bibliography at the end of the paper contains references to papers, conference proceedings and theses/dissertations on the subject that were published between 1977‐1998. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, ferrites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.

The coupled set of non‐linear 2D diffusion equations for donor and acceptor type impurities with initial and appropriated boundary conditions is solved by an implicit locally‐one dimensional finite difference method. Numerical experiments have been made to achieve a reasonable trade‐off between the desired accuracy and the CPU time. The algorithm was implemented to the process module of the 2‐D integrated process and device modeling system IMPEDANCE 2.0.