A discontinuous interpolated finite volume approximation of semilinear elliptic optimal control problems1. Issue 6 (24th July 2017)

• Record Type: Journal Article
• Authors: Sandilya, Ruchi; Kumar, Sarvesh
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 6(2017:Nov.)
• Page Start: 2090
• Page End: 2113
• Publication Date: 2017-07-24
• Subjects: discontinuous finite volume methods -- interpolated coefficients -- semilinear elliptic optimal control problems -- variational discretization -- piecewise constant and linear discretizations -- a priori error estimates -- numerical experiments; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22181
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, we describe a discontinuous finite volume method with interpolated coefficients for the numerical approximation of the distributed optimal control problem governed by a class of semilinear elliptic equations with control constraints. The proposed distributed control problem involves three unknown variable: control, state and costate. For the approximation of control, we have adopted three different methodologies: variational discretization, piecewise constant and piecewise linear discretization, while the approximation of state and costate variables is based on discontinuous piecewise linear polynomials. As the resulted scheme is non‐symmetric, optimize‐then‐discretize approach is used to approximate the control problem. Optimal a priori error estimates in suitable natural norms for state, costate and control variables are derived. Moreover, numerical experiments are presented to support the derived theoretical results. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2090–2113, 2017