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Volume 10, Issue 4
An EDG Method for Distributed Optimal Control of Elliptic PDEs

Xiao Zhang, Yangwen Zhang & John Singler

Adv. Appl. Math. Mech., 10 (2018), pp. 797-818.

Published online: 2018-06

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  • Abstract

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state, and the optimal control, and suboptimal estimates for the fluxes. We present numerical experiments to confirm our theoretical results.

  • AMS Subject Headings

65N30, 49M25

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COPYRIGHT: © Global Science Press

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@Article{AAMM-10-797, author = {Zhang , XiaoZhang , Yangwen and Singler , John}, title = {An EDG Method for Distributed Optimal Control of Elliptic PDEs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {4}, pages = {797--818}, abstract = {

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state, and the optimal control, and suboptimal estimates for the fluxes. We present numerical experiments to confirm our theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2017-0223}, url = {http://global-sci.org/intro/article_detail/aamm/12496.html} }
TY - JOUR T1 - An EDG Method for Distributed Optimal Control of Elliptic PDEs AU - Zhang , Xiao AU - Zhang , Yangwen AU - Singler , John JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 797 EP - 818 PY - 2018 DA - 2018/06 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2017-0223 UR - https://global-sci.org/intro/article_detail/aamm/12496.html KW - Distributed optimal control, elliptic PDEs, embedded discontinuous Galerkin method, error analysis. AB -

We consider a distributed optimal control problem governed by an elliptic PDE, and propose an embedded discontinuous Galerkin (EDG) method to approximate the solution. We derive optimal a priori error estimates for the state, dual state, and the optimal control, and suboptimal estimates for the fluxes. We present numerical experiments to confirm our theoretical results.

Zhang , XiaoZhang , Yangwen and Singler , John. (2018). An EDG Method for Distributed Optimal Control of Elliptic PDEs. Advances in Applied Mathematics and Mechanics. 10 (4). 797-818. doi:10.4208/aamm.OA-2017-0223
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