抛物最优控制问题的有限体积元误差估计

Error estimate of finite volume elements for parabolic optimal control problems

采用拉格朗日方法推导出抛物最优控制问题的最优性条件,然后运用有限体积元和变分离散相结合的方法得到离散的最优性条件,给出最优解在L2范数意义下的误差估计,并通过数值算例验证了误差估计的理论结果.

This paper presents the finite volume element method(FVEM)to solve the optimal control problems governed by the parabolic equation.The optimality conditions are given by the Lagrange method.Variational discretization and the FVEM are applied to discretize the optimality conditions.Optimal order error estimates in the sense of L 2 norm are obtained.Numerical examples are provided to confirm the effectiveness of the method and the theoretical results.