Equivalence of two strictly bounding approaches for goal-oriented error estimation

GUO Mengwu; ZHONG Hongzhi

doi:10.16511/j.cnki.qhdxxb.2017.25.005

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Journal of Tsinghua University(Science and Technology) ›› 2017, Vol. 57 ›› Issue (4) : 362-368. DOI: 10.16511/j.cnki.qhdxxb.2017.25.005

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Equivalence of two strictly bounding approaches for goal-oriented error estimation

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Abstract

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.

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numerical methods for partial differential equations (PDEs) / a posteriori error estimation / goal-oriented error estimation / constitutive relation error / constrained optimization with convex objective functions / strict bounds / complementary energy theorem

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GUO Mengwu, ZHONG Hongzhi. Equivalence of two strictly bounding approaches for goal-oriented error estimation[J]. Journal of Tsinghua University(Science and Technology). 2017, 57(4): 362-368 https://doi.org/10.16511/j.cnki.qhdxxb.2017.25.005

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