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In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order k (k≥1). L2 and L∞-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for fourth order elliptic control problems.
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참고문헌 (22)
참고문헌 신청
B. J. Li / 2007 / On gradient-type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi-harmonic equation / A
C. Johnson / 1973 / On the convergence of a mixed finite-element method for plate bending problems / Numer. Math 21 : 43 ~ 62
F. Brezzi / 1991 / Mixed and Hybrid Finite Element Methods / Springer-Verlag
H. Bium / 1990 / On mixed finite element methods in plate bending analysis / Comput. Mech 6 : 221 ~ 236
H. Chen / 2000 / L∞-convergence of mixed finite element method for laplacian operator / Korean J. Comput. Appl. Math 7 (1) : 61 ~ 82
C. Johnson / 1973 / On the convergence of a mixed finite-element method for plate bending problems / Numer. Math 21 : 43 ~ 62
F. Brezzi / 1991 / Mixed and Hybrid Finite Element Methods / Springer-Verlag
H. Bium / 1990 / On mixed finite element methods in plate bending analysis / Comput. Mech 6 : 221 ~ 236
H. Chen / 2000 / L∞-convergence of mixed finite element method for laplacian operator / Korean J. Comput. Appl. Math 7 (1) : 61 ~ 82
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