Approximate Solutions and Error Bounds for Quadiliniear Elliptic Boundary Value Problems

Abstract

An error bound for a quasilinear elliptic boundary value problem (including the case of nonlinear differential boundary conditions) is obtained as a positively weighted sum of the absolute defects of the operator equations. Once an approximate solution is computed, using linear programming, by minimizing this error bound over a discrete grid, a corresponding realistic error bound over the whole domain of definition can also be obtained by solving an associated linear program.