两种严格界面向目标误差估计方法的等价性

For model verification which is mainly focused on the control of discretization errors of numerical results, a posteriori error estimation plays an important role in various numerical tools such as the finite element method. The outputs of interest are usually converted into integral functionals over the problem domain for a posteriori error analysis. Among the available techniques for goal-oriented error estimation, only two approaches, the constitutive relation error estimation and the constrained optimization method with convex objective functions, have been claimed to be able to offer guaranteed strict upper and lower bounds for the errors in quantities of interest. The two approaches are briefly reviewed and the equivalence of their formulation and principle is given. Both approaches are shown to be essentially based on the complementary energy theorem. The equivalence of the two approaches is instrumental in simplification of error estimation and extension of applications into more complex problems.