Estimation of the Accuracy of Finite-Element Petrov–Galerkin Method in Integrating the One-Dimensional Stationary Convection-Diffusion-Reaction Equation

Abstract

The accuracy and convergence of the numerical solutions of a stationary one-dimensional linear convection-diffusion-reaction equation (with Dirichlet boundary conditions) by the Petrov–Galerkin finiteelement method with piecewise-linear basis functions and piecewise-quadratic weighting functions are analyzed and the accuracy estimates of the method are obtained in certain norms depending on the choice of the collection of stabilization parameters of weight functions.