Error estimates for a splitting integrator for abstract semilinear boundary coupled systems

A Posteriori Error Estimates for Semilinear Boundary Control Problems

In this paper we study the finite element approximation for boundary control problems governed by semilinear elliptic equations. Optimal control problems are very important model in science and engineering numerical simulation. They have various physical backgrounds in many practical applications. Finite element approximation of optimal control problems plays a very important role in the numeri...

Error Estimates for a Semilinear Elliptic

Error Estimates for the Numerical Approximation of Dirichlet Boundary Control for Semilinear Elliptic Equations

We study the numerical approximation of boundary optimal control problems governed by semilinear elliptic partial differential equations with pointwise constraints on the control. The control is the trace of the state on the boundary of the domain, which is assumed to be a convex, polygonal, open set in R. Piecewise linear finite elements are used to approximate the control as well as the state...

Blow-up estimates for a semilinear coupled parabolic system

This work deals with a semilinear parabolic systemwhich is coupled both in the equations and in the boundary conditions. The blow-up phenomena of its positive solutions are studied using the scaling method, the Green function and Schauder estimates. The upper and lower bounds of blow-up rates are then obtained. Moreover we show the influences of the reaction terms and the boundary absorption te...

Error Estimates for the Numerical Approximation of Boundary Semilinear Elliptic Control Problems. Continuous Piecewise Linear Approximations

We discuss error estimates for the numerical analysis of Neumann boundary control problems. We present some known results about piecewise constant approximations of the control and introduce some new results about continuous piecewise linear approximations. We obtain the rates of convergence in i ^ ( r ) . Error estimates in the uniform norm are also obtained. We also discuss the semidiscretiza...