Analysis of Generalised Galerkin methods in the numerical solution of elliptic equations

摘要

AbstractThe Petrov‐Galerkin projection method is outlined for the solution of the linear elliptic equationLu=fwith homogeneous boundary conditions. By choosing appropriate finite dimensional trial and test spaces, the methods of weighted residuals, collocation, andH1Galerkin can be interpreted within the Petrov‐Galerkin projection method framework.The important question of how best to choose the trial and test functions to suit a particular type of problem is then discussed. Objective criteria associated with the matrix which governs the Petrov‐Galerkin numerical process are pro