A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as is examined.
A distributed optimal control problem for evolutionary Stokes flows is
studied a pseudocompressibility formulation.
Several results concerning the analysis of the velocity tracking problem are
presented. Semidiscrete finite element error estimates for the corresponding
optimality system are derived based on estimates for the penalized
Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the
convergence of the solutions of the penalized optimality systems
as ε → 0 is examined.
...
A discontinuous Galerkin finite element method for an optimal
control problem related to semilinear parabolic PDE's is examined.
The schemes under consideration are discontinuous in time but
conforming in space. Convergence of discrete schemes of arbitrary
order is proven. In addition, the convergence of discontinuous
Galerkin approximations of the associated optimality system to the
solutions of the continuous optimality system is shown. The proof
is based on stability estimates at arbitrary time...
We propose and analyze a semi Lagrangian method for the
convection-diffusion equation. Error estimates for both semi and
fully discrete finite element approximations are obtained for
convection dominated flows. The estimates are posed in terms of
the projections constructed in [Chrysafinos and Walkington, (2006) 2478–2499; Chrysafinos and Walkington, (2006) 349–366] and the
dependence of various constants upon the diffusion parameter is
characterized. Error estimates independent of...
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the...
Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic
PDEs are examined. The schemes under consideration are discontinuous in time but
conforming in space and of arbitrary order. Stability estimates are presented in the
natural energy norms and at arbitrary times, under minimal regularity assumptions.
Space-time error estimates of arbitrary order are derived, provided that the natural
parabolic regularity is present....
Download Results (CSV)