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Displaying similar documents to “Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations.”

Mortar spectral element discretization of the Laplace and Darcy equations with discontinuous coefficients

Zakaria Belhachmi, Christine Bernardi, Andreas Karageorghis (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with the mortar spectral element discretization of two equivalent problems, the Laplace equation and the Darcy system, in a domain which corresponds to a nonhomogeneous anisotropic medium. The numerical analysis of the discretization leads to optimal error estimates and the numerical experiments that we present enable us to verify its efficiency.

Optimal control and numerical adaptivity for advection–diffusion equations

Luca Dede', Alfio Quarteroni (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates...