Summary
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.
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Mittelmann, H.D. On the efficient solution of nonlinear finite element equations I. Numer. Math. 35, 277–291 (1980). https://doi.org/10.1007/BF01396413
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DOI: https://doi.org/10.1007/BF01396413