Estimation of the error in the reduced basis method solution of nonlinear equations. (English) Zbl 0586.65040

Porsching, T. A.

Math. Comput. 45, 487-496 (1985).

The subject of this paper is the error analysis of the reduced basis method (RBM) - a composite projection-continuation method for the solution of systems of nonlinear equations arising most often from finite element approximations of systems of partial differential equations. The essense of the RBM is to yield accurate approximations of the solution of the original system by way of solving another system of much lower dimension. Projections on three different subspaces are studied and corresponding approximation errors turn out to be of the same order. Comparative numerical results from earlier papers are discussed.

Reviewer: N.Vulchanov

MSC:

65H10	Numerical computation of solutions to systems of equations
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

reduced basis method; projection-continuation method; finite element; errors; numerical results