TY - JOUR
T1 - Higher Order Triangular Mixed Finite Element Methods for Semilinear Quadratic Optimal Control Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 180
EP - 196
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.42s.4
UR - https://global-sci.org/intro/article_detail/nmtma/5964.html
KW - A priori error estimates, semilinear optimal control problems, higher order triangular elements, mixed finite element methods.
AB - <p style="text-align: justify;">In this paper, we investigate a priori error estimates for the
quadratic optimal control problems governed by semilinear elliptic
partial differential equations using higher order triangular mixed
finite element methods. The state and the co-state are approximated
by the order $k$ Raviart-Thomas mixed finite element spaces and the
control is approximated by piecewise polynomials of order $k$ ($k\geq 0$). A priori error estimates for the mixed finite element
approximation of semilinear control problems are obtained. Finally,
we present some numerical examples which confirm our theoretical
results.</p>