On the efficient solution of nonlinear finite element equations. A fast numerical method is presented for the solution of nonlinear algebraic systems which arise from discretizations of elliptic boundary value problems. A simplified relaxation algorithm which needs no information about the Jacobian of the system is combined with a correspondingly modified conjugate gradient method. A global convergence proof is given and the number of operations required is compared with that of other algorithms which are equally applicable to a large class of problems. Numerical results verify the efficiency for some typical examples.
- Subject Classifications: AMS(MOS), 65N30, 65H10, 65K10, CR: 5.17, 5.15
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics