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Error analysis of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation
Author(s) -
Liu Huipo,
Wang Shuanghu,
Han Hongbin,
Yuan Lan
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22149
Subject(s) - mathematics , finite element method , discontinuous galerkin method , discretization , a priori and a posteriori , galerkin method , piecewise , partial differential equation , control variable , optimal control , mixed finite element method , convection–diffusion equation , piecewise linear function , mathematical analysis , mathematical optimization , physics , philosophy , statistics , epistemology , thermodynamics
This article discusses a priori and a posteriori error estimates of discontinuous Galerkin finite element method for optimal control problem governed by the transport equation. We use variational discretization concept to discretize the control variable and discontinuous piecewise linear finite elements to approximate the state and costate variable. Based on the error estimates of discontinuous Galerkin finite element method for the transport equation, we get a priori and a posteriori error estimates for the transport equation optimal control problem. Finally, two numerical experiments are carried out to confirm the theoretical analysis.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1493–1512, 2017