Papers by Bacuta Constantin
We consider discretization on overlapping non-matching grids for elliptic equations by using the ... more We consider discretization on overlapping non-matching grids for elliptic equations by using the Schwartz alternating (SA) method. We investigate the dependence between the angle of partition of unity (PU) subspaces, the condition number of the stiffness matrix, and the rate of convergence. The aim of the paper is to find strategies to choose optimal or quasi-optimal partition of unity set of functions for PU discretizaions for elliptic problems on overlapping non-matching grids.
Computers & Mathematics with Applications, 2016
We present a Saddle Point Least Squares (SPLS) method for discretizing second order elliptic prob... more We present a Saddle Point Least Squares (SPLS) method for discretizing second order elliptic problems written as primal mixed variational formulations. A stability LBB condition and a data compatibility condition at the continuous level are automatically satisfied. The proposed discretization method follows a general SPLS approach and has the advantage that a discrete inf − sup condition is automatically satisfied for standard choices of the test and trial spaces. For the proposed iterative processes a nodal basis for the trial space is not required. Efficient preconditioning techniques that involve inversion only on the test space can be considered. Stability and approximation properties for two choices of discrete spaces are investigated. Applications of the new approach include discretization of second order problems with highly oscillatory coefficient, interface problems, and higher order approximation of the flux for elliptic problems with smooth coefficients.
We consider the model Poisson problem −∆u = f ∈ Ω, u = g on ∂Ω, where Ω is a bounded polyhedral d... more We consider the model Poisson problem −∆u = f ∈ Ω, u = g on ∂Ω, where Ω is a bounded polyhedral domain in R n. The objective of the paper is twofold. The first objective is to review the well posedness and the regularity of our model problem using appropriate weighted spaces for the data and the solution. We use these results to derive the domain of the Laplace operator with zero boundary conditions on a concave domain, which seems not to have been fully investigated before. We also mention some extensions of our results to interface problems for the Elasticity equation. The second objective is to illustrate how anisotropic weighted regularity results for the Laplace operator in 3D are used in designing efficient finite element discretizations of elliptic boundary value problems, with the focus on the efficient discretization of the Poisson problem on polyhedral domains in R 3 , following Numer. Funct. Anal. Optim., 28(7-8):775-824, 2007. The anisotropic weighted regularity results described and used in the second part of the paper are a consequence of the well-posedness results in (isotropically) weighted Sobolev spaces described in the first part of the paper. The paper is based on the talk by the last named author at the Congress of Romanian Mathematicians, Brasov 2011, and is largely a survey paper.
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Papers by Bacuta Constantin