For a class of nonlinear elliptic boundary value problems in divergence form, we construct some general elliptic inequalities for appropriate combinations of u(x) and |∇u|2, where u(x) are the solutions of our problems. From these inequalities, we derive, using Hopf ’s maximum principles, some maximum principles for the appropriate combinations of u(x) and |∇u|2, and we list a few examples of p...

In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearization technique and the cascadic multigrid approach. The error analysis and the complexity analysis for the proposed method are carried out based on the two-grid theory and its multilevel extension. A superconvergence result for the multilevel linearizati...

A class of generalized approximate inverse finite element matrix algorithmic methods for solving nonlinear parabolic and elliptic PDE’s, is presented. Fully parameterized singularly perturbed non-linear parabolic and elliptic PDE’s are considered and explicit preconditioned generalized conjugate gradient type schemes are presented for the efficient solution of the resulting nonlinear systems of...