Error analysis of H1 gradient method for topology optimization problems of continua

Abstract

The present paper describes the result of the error estimation of a numerical solution to topology optimization problems of domains in which boundary value problems are defined. In the previous paper, we formulated a problem by using density as a design variable, presented a regular solution, and called it the H1 gradient method. The main result in this paper is the proof of the first order convergence in the H1 norm of the solution in the H1 gradient method with respect to the size of the finite elements if first order elements are used for the design and state variables.