Error bounds for a Dirichlet boundary control problem based on energy spaces
Authors:
Sudipto Chowdhury, Thirupathi Gudi and A. K. Nandakumaran
Journal:
Math. Comp. 86 (2017), 1103-1126
MSC (2010):
Primary 65N30, 65N15, 65N12, 65K10
DOI:
https://doi.org/10.1090/mcom/3125
Published electronically:
June 20, 2016
MathSciNet review:
3614013
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: 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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Additional Information
Sudipto Chowdhury
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Email:
sudipto10@math.iisc.ernet.in
Thirupathi Gudi
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Email:
gudi@math.iisc.ernet.in
A. K. Nandakumaran
Affiliation:
Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India
Email:
nands@math.iisc.ernet.in
Keywords:
Optimal control,
Dirichlet control,
finite element,
optimal error estimate,
adaptive finite element,
a posteriori estimates
Received by editor(s):
May 19, 2015
Received by editor(s) in revised form:
August 27, 2015, and October 7, 2015
Published electronically:
June 20, 2016
Article copyright:
© Copyright 2016
American Mathematical Society