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

Xiao Zhang, Yangwen Zhang & John Singler

DOI: 10.4208/aamm.OA-2017-0223

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.

  • Keywords

Distributed optimal control, elliptic PDEs, embedded discontinuous Galerkin method, error analysis.

  • AMS Subject Headings

65N30, 49M25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-10-797, author = {}, 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 JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 797 EP - 818 PY - 2018 DA - 2018/06 SN - 10 DO - http://dor.org/10.4208/aamm.OA-2017-0223 UR - https://global-sci.org/intro/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.

Xiao Zhang, Yangwen Zhang & John Singler. (2020). 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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