22,215 research outputs found
A residual based snapshot location strategy for POD in distributed optimal control of linear parabolic equations
In this paper we study the approximation of a distributed optimal control
problem for linear para\-bolic PDEs with model order reduction based on Proper
Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the
basis functions are obtained upon information contained in time snapshots of
the parabolic PDE related to given input data. In the present work we show that
for POD-MOR in optimal control of parabolic equations it is important to have
knowledge about the controlled system at the right time instances. For the
determination of the time instances (snapshot locations) we propose an
a-posteriori error control concept which is based on a reformulation of the
optimality system of the underlying optimal control problem as a second order
in time and fourth order in space elliptic system which is approximated by a
space-time finite element method. Finally, we present numerical tests to
illustrate our approach and to show the effectiveness of the method in
comparison to existing approaches
Flux form Semi-Lagrangian methods for parabolic problems
A semi-Lagrangian method for parabolic problems is proposed, that extends
previous work by the authors to achieve a fully conservative, flux-form
discretization of linear and nonlinear diffusion equations. A basic consistency
and convergence analysis are proposed. Numerical examples validate the proposed
method and display its potential for consistent semi-Lagrangian discretization
of advection--diffusion and nonlinear parabolic problems
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