Numerical solution of nonlinear elliptic systems by block monotone iterations

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...

Numerical solution of nonlinear integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions

In this paper, we use a combination of Legendre and Block-Pulse functionson the interval [0; 1] to solve the nonlinear integral equation of the second kind.The nonlinear part of the integral equation is approximated by Hybrid Legen-dre Block-Pulse functions, and the nonlinear integral equation is reduced to asystem of nonlinear equations. We give some numerical examples. To showapplicability of...

Numerical solution of fully nonlinear elliptic equations by Böhmer's method

We present an implementation of Böhmer’s finite element method for fully nonlinear elliptic partial differential equations on convex polygonal domains, based on a modified Argyris element and BernsteinBézier techniques. Our numerical experiments for several test problems, involving the classical Monge-Ampère equation and an unconditionally elliptic equation, confirm the convergence and error bo...

Numerical stability of iterations for solution of nonlinear equations and large linear systems

We survey some recent results on the problem of numerical stability of iterations for the solution of nonlinear equations F(x) = 0 and large linear systems Ax+g = 0 where A = A is positive definite. For systems of nonlinear equations we assume that the function F depends on a so called data vector F(x) = F(x;d). We define the condition number cond(F;d), numerical stability and well-behavior of ...

Solvability of monotone systems of fully nonlinear elliptic PDE's