Discontinuous galerkin methods for time-dependent convection dominated optimal control problems

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2011

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Akman, Tuğba

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Distributed optimal control problems with transient convection dominated diffusion convection reaction equations are considered. The problem is discretized in space by using three types of discontinuous Galerkin (DG) method: symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), incomplete interior penalty Galerkin (IIPG). For time discretization, Crank-Nicolson and backward Euler methods are used. The discretize-then-optimize approach is used to obtain the finite dimensional problem. For one-dimensional unconstrained problem, Newton-Conjugate Gradient method with Armijo line-search. For two-dimensional control constrained problem, active-set method is applied. A priori error estimates are derived for full discretized optimal control problem. Numerical results for one and two-dimensional distributed optimal control problems for diffusion convection equations with boundary layers confirm the predicted orders derived by a priori error estimates.

Subject Keywords

Galerkin methods.

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http://etd.lib.metu.edu.tr/upload/12613394/index.pdf
https://hdl.handle.net/11511/20617

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Graduate School of Applied Mathematics, Thesis

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Citation Formats

T. Akman, “Discontinuous galerkin methods for time-dependent convection dominated optimal control problems,” M.S. - Master of Science, Middle East Technical University, 2011.