Optimal Boundary Estimates for Stokes Systems in Homogenization Theory

Homogenization of Stokes Systems and Uniform Regularity Estimates

Compression Techniques for Boundary Integral Equations - Asymptotically Optimal Complexity Estimates

Matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the num...

Homogenization of the Stokes equation with mixed boundary condition in a porous medium

Boundary Value Problems and Optimal Boundary Control for the Navier–stokes System: the Two-dimensional Case∗

We study optimal boundary control problems for the two-dimensional Navier–Stokes equations in an unbounded domain. Control is effected through the Dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with minimal regularity satisfying the energy estimates. An objective of interest is the drag functional. We first establish three important results for inho...

Homogenization and boundary layer

This paper deals with the homogenization of elliptic systems with Dirichlet boundary condition, when the coefficients of both the system and the boundary data are ε-periodic. We show that, as ε → 0, the solutions converge in L2 with a power rate in ε, and identify the homogenized limit system. Due to a boundary layer phenomenon, this homogenized system depends in a non trivial way on the bounda...