Error bounds for a Dirichlet boundary control problem based on energy spaces | Zendy

Sudipto Chowdhury | Zendy; Thirupathi Gudi | Zendy; A. K. Nandakumaran | Zendy

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Error bounds for a Dirichlet boundary control problem based on energy spaces

Author(s) -

Sudipto Chowdhury,

Thirupathi Gudi,

A. K. Nandakumaran

Publication year - 2015

Publication title -

mathematics of computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.95

H-Index - 103

eISSN - 1088-6842

pISSN - 0025-5718

DOI - 10.1090/mcom/3125

Subject(s) - mathematics , a priori and a posteriori , estimator , norm (philosophy) , dirichlet distribution , finite element method , dirichlet boundary condition , dirichlet problem , boundary value problem , numerical analysis , energy (signal processing) , boundary (topology) , space (punctuation) , mathematical optimization , mathematical analysis , computer science , statistics , philosophy , physics , epistemology , political science , law , thermodynamics , operating system

In this article, an alternative energy-space based approach is proposed for the Dirichlet boundary control problem and then a finite-element based numerical method is designed and analyzed for its numerical approximation. A priori error estimates of optimal order in the energy norm and the L-2-norm are derived. Moreover, a reliable and efficient a posteriori error estimator is derived with the help of an auxiliary problem. The theoretical results are illustrated by the numerical experiments

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