PROPERTIES OF SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS USING FINITE ELEMENT METHODS

Abstract

This chapter focuses on properties of solutions of nonlinear partial differential equations using finite element methods. It presents estimates of bounds and zeros of classical solutions of some nonlinear partial differential equations in bounded regions R a subset of En. Estimates do not depend upon boundary conditions imposed on the classical solutions of such partial differential equations. However, such estimates obtained will depend upon the class of trial functions defined on a finite element mesh of R. Methods used are in contrast to those of actually attempting to compute such a classical solution in detail throughout large regions R contained in Euclidean n-space En and, thus, provide rapid initial estimates of such properties of classical solutions. The chapter describes second-order nonlinear elliptic partial differential equations.