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Volume 9, Issue 1
Superconvergence of $H$1-Galerkin Mixed Finite Element Methods for Elliptic Optimal Control Problems

Chunmei Liu, Tianliang Hou & Yin Yang

DOI: 10.4208/eajam.150117.070618

East Asian J. Appl. Math., 9 (2019), pp. 87-101.

Published online: 2019-01

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  • Abstract

The convergence of $H$1-Galerkin mixed finite element methods for elliptic optimal control problems is studied and postprocessing operators are used to establish the superconvergence for control, state and adjoint state variables. A numerical example confirms the validity of theoretical results.

  • Keywords

Elliptic equations, optimal control problems, superconvergence, $H^1$-Galerkin mixed finite element methods.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-87, author = {Chunmei Liu, Tianliang Hou and Yin Yang}, title = {Superconvergence of $H$1-Galerkin Mixed Finite Element Methods for Elliptic Optimal Control Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {1}, pages = {87--101}, abstract = {

The convergence of $H$1-Galerkin mixed finite element methods for elliptic optimal control problems is studied and postprocessing operators are used to establish the superconvergence for control, state and adjoint state variables. A numerical example confirms the validity of theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150117.070618}, url = {http://global-sci.org/intro/article_detail/eajam/12936.html} }
TY - JOUR T1 - Superconvergence of $H$1-Galerkin Mixed Finite Element Methods for Elliptic Optimal Control Problems AU - Chunmei Liu, Tianliang Hou & Yin Yang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 87 EP - 101 PY - 2019 DA - 2019/01 SN - 9 DO - http://doi.org/10.4208/eajam.150117.070618 UR - https://global-sci.org/intro/article_detail/eajam/12936.html KW - Elliptic equations, optimal control problems, superconvergence, $H^1$-Galerkin mixed finite element methods. AB -

The convergence of $H$1-Galerkin mixed finite element methods for elliptic optimal control problems is studied and postprocessing operators are used to establish the superconvergence for control, state and adjoint state variables. A numerical example confirms the validity of theoretical results.

Chunmei Liu, Tianliang Hou and Yin Yang. (2019). Superconvergence of $H$1-Galerkin Mixed Finite Element Methods for Elliptic Optimal Control Problems. East Asian Journal on Applied Mathematics. 9 (1). 87-101. doi:10.4208/eajam.150117.070618
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