2013 年 5 巻 p. 29-32
We present an error estimation for the H1 gradient method, which provides numerical solutions to the shape-optimization problem of the domain in which a boundary value problem is defined. The main result is that if second-order elements are used for the solutions of the main and adjoint boundary value problems to evaluate the shape derivative, and the first-order elements are used for the solution of domain variation in the boundary value problem of the H1 gradient method, then we obtain first-order convergence of the solution of the domain variation with respect to the size of the finite elements.
