Temat: approximation equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Dynamic programming approach to structural optimization problem - numerical algorithm
Autorzy:: Fulmański, P.
Nowakowski, A.
Pustelnik, J.
Powiązania:: https://bibliotekanauki.pl/articles/255706.pdf
Data publikacji:: 2014
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: elliptic equations
optimal shape control
structural optimization
stationary Navier-Stokes equations
dynamic programming
sufficient optimality condition
numerical approximation
Opis:: In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
Źródło:: Opuscula Mathematica; 2014, 34, 4; 699-724
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
Autorzy:: Meyer, C.
Powiązania:: https://bibliotekanauki.pl/articles/971011.pdf
Data publikacji:: 2008
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: równanie eliptyczne
aproksymacja numeryczna
linear quadratic optimal control problems
elliptic equations
state constraints
numerical approximation
Opis:: We consider a linear-quadratic elliptic optimal control problem with pointwise state constraints. The problem is fully discretized using linear ansatz functions for state and control. Based on a Slater-type argument, we investigate the approximation behavior for mesh size tending to zero. The obtained convergence order for the L²-error of the control and for H 1-error of the state is 1 - ε in the two-dimensional case and 1/2 - ε in three dimensions, provided that the domain satisfies certain regularity assumptions. In a second step, a state-constrained problem with additional control constraints is considered. Here, the control is discretized by constant ansatz functions. It is shown that the convergence theory can be adapted to this case yielding the same order of convergence. The theoretical findings are confirmed by numerical examples.
Źródło:: Control and Cybernetics; 2008, 37, 1; 51-83
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Finite element error analysis for state-constrained optimal control of the Stokes equations
Autorzy:: Los Reyes, J. C. de
Meyer, C.
Vexler, B.
Powiązania:: https://bibliotekanauki.pl/articles/969607.pdf
Data publikacji:: 2008
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: równanie Stokesa
aproksymacja numeryczna
element skończony
linear quadratic optimal control problems
Stokes equations
state constraints
numerical approximation
finite elements
Opis:: An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.
Źródło:: Control and Cybernetics; 2008, 37, 2; 251-284
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

Artykuł

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