<i>A posteriori</i> error estimates of characteristic mixed finite elements for convection-diffusion control problems-Reference-Cited by-同舟云学术

A posteriori error estimates of characteristic mixed finite elements for convection-diffusion control problems

Published:2022-01-01 Issue:1 Volume:20 Page:629-645
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Tang Yuelong¹,Hua Yuchun¹

Affiliation:

1. Department of Computational Science, College of Science, Hunan University of Science and Engineering , Yongzhou 425100 , P. R. China

Abstract

Abstract In this article, we consider fully discrete characteristic mixed finite elements for convection-diffusion optimal control problems. We use the characteristic line method to treat the hyperbolic part of the state equation as a directional derivative. The state and the co-state are discretized by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions. Using some proper duality problems, we derive a posteriori error estimates for the scalar functions. Such estimates are not available in the literature. A numerical example is presented to validate the theoretical results.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2022-0053/pdf

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