On finite element methods for convection dominated phenomena
Abstract
An attempt is made to give a theoretical justification of several types of finite element approximations to the initial boundary value problems of firstorder linear hyperbolic equations. The proposed approximate scheme is obtained by the piecewise linear continuous finite element method for the space variable and the Eulertype stepbystep integration method for the time variable. An artificial viscosity technique and upstreamtype methods are discussed in the framework of Lsquared theory. Attention is given to the convergence and the error estimate of the approximate solutions.
 Publication:

Mathematical Methods in the Applied Sciences
 Pub Date:
 1982
 DOI:
 10.1002/mma.1670040108
 Bibcode:
 1982MMAS....4...98K
 Keywords:

 Boundary Value Problems;
 Convective Flow;
 Finite Element Method;
 Galerkin Method;
 Hyperbolic Differential Equations;
 Linear Equations;
 Approximation;
 Computational Fluid Dynamics;
 Convergence;
 Error Analysis;
 Linearization;
 Operators (Mathematics);
 Viscous Flow;
 Fluid Mechanics and Heat Transfer