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 first-order linear hyperbolic equations. The proposed approximate scheme is obtained by the piecewise linear continuous finite element method for the space variable and the Euler-type step-by-step integration method for the time variable. An artificial viscosity technique and upstream-type methods are discussed in the framework of L-squared 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