A priori error estimates and superconvergence of $P_0^2-P_1$ mixed finite element methods for elliptic boundary control problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 1, pp. 63-76
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In this paper, we discuss a priori error estimates and superconvergence of $P_0^2-P_1$ mixed finite element methods for elliptic boundary control problems. The state variables and co-state variables are approximated by a $P_0^2-P_1$ (velocity-pressure) pair and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates for the control variable, the state variables and the co-state variables. Then we obtain a superconvergence result for the control variable by using postprocessing projection operator.
@article{SJVM_2021_24_1_a5,
author = {C. Xu},
title = {A priori error estimates and superconvergence of $P_0^2-P_1$ mixed finite element methods for elliptic boundary control problems},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {63--76},
publisher = {mathdoc},
volume = {24},
number = {1},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a5/}
}
TY - JOUR AU - C. Xu TI - A priori error estimates and superconvergence of $P_0^2-P_1$ mixed finite element methods for elliptic boundary control problems JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2021 SP - 63 EP - 76 VL - 24 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a5/ LA - ru ID - SJVM_2021_24_1_a5 ER -
%0 Journal Article %A C. Xu %T A priori error estimates and superconvergence of $P_0^2-P_1$ mixed finite element methods for elliptic boundary control problems %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2021 %P 63-76 %V 24 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a5/ %G ru %F SJVM_2021_24_1_a5
C. Xu. A priori error estimates and superconvergence of $P_0^2-P_1$ mixed finite element methods for elliptic boundary control problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 24 (2021) no. 1, pp. 63-76. http://geodesic.mathdoc.fr/item/SJVM_2021_24_1_a5/