Error Estimates to A Kind of Boundary Value Problem about An Elliptic Differential Equation with Variable Coefficient

Abstract

A kind of boundary value problem about a second-order elliptic differential equation with variable coefficient is discussed indirectly by transforming it as the second kind of variational inequality form. Using regularization method, the variational inequality is formulated as an equal variational equation, which can be made discrete by the finite element method. Abstract error estimate and the error estimates of the approximation are derived under the energy norm and 2 L -norm.