In this work we present several finite element techniques to solve the convection-diffusion equation when the Péclet number is high, tha is, when diffusion is very small. The basic finite element formulation employed here is the Streamline-Upwind-Petrov-Galerkin (SUPG). A thorough description of this approach is presented in Chapter 1. Chapter 2 deals with the application of the generalized trapezoidal rule to advance in time for the transient equation. A complete stability and accuracy analysis is performed for the explicit Euler scheme, both using linear and quadratic finite elements. Chapter 3 is concerned with the problem of removing the localized oscillations that remain about abrupt layers of the solution.

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Published on 10/01/19
Submitted on 10/01/19

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