A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
نویسندگان
چکیده
منابع مشابه
A FEM for an Optimal Control Problem of Fractional Powers of Elliptic Operators
We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-toNeumann map for a nonuniformly elliptic problem. Thus, we consider an equivalent formulation with a nonuniformly elliptic operator as state equation. The rapid decay of the solution to this problem suggests a...
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A boundary value problem for a fractional power of the second-order elliptic operator is considered. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. Stability conditions are obtained for the fully discrete schemes under the consideration. The numerical results are ...
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15 صفحه اولNumerical approximation of fractional powers of elliptic operators
We present and study a novel numerical algorithm to approximate the action of T := L where L is a symmetric and positive definite unbounded operator on a Hilbert space H0. The numerical method is based on a representation formula for T in terms of Bochner integrals involving (I + tL) for t ∈ (0,∞). To develop an approximation to T , we introduce a finite element approximation Lh to L and base o...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2015
ISSN: 0363-0129,1095-7138
DOI: 10.1137/140975061