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Journals and Conferences
This paper deals with the finite element approximation of Hamilton-Jacobi-Bellman equations. We establish a convergence and a quasi-optimal Lm -error estimate, involving a weakly coupled system of quasi-variational inequalities for the solution of which an iterative scheme of monotone kind is introduced and analyzed.
We provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for second-order elliptic obstacle problem. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The grid points on the subdomain boundaries need not match the grid points from the other… (More)
This paper deals with a system of quasi-variational inequalities with noncoercive operators. We prove the existence of a unique weak solution using a lower and upper solutions approach. Furthermore, by means of a Banach’s fixed point approach, we also prove that the standard finite element approximation applied to this system is quasi-optimally accurate in… (More)
This paper is devoted to the approximation by a piecewise linear finite element method of a noncoercive system of elliptic quasi-variational inequalities arising in the management of energy production. A quasi-optimal L∞ error estimate is established, using the concept of subsolution.
whereΩ is a bounded smooth domain ofRN ,N ≥ 1, with boundary ∂Ω,ai(u,v) are J-elliptic bilinear forms continuous on H1(Ω)×H1(Ω), (·,·) is the inner product in L2(Ω), and f i are J-regular functions. This system, introduced by Bensoussan and Lions (see ), arises in the management of energy production problems where J-units are involved (see  and the… (More)
In this paper we provide a simple proof to derive L∞-error estimate for a noncoercive system of quasi-variational inequalities related to the management of energy production. The key idea is a discrete L∞-stability property owned by the corresponding coercive problem.
Keywords: Elliptic PDEs Schwarz alternating method Nonmatching grids Finite element L 1 – error estimate a b s t r a c t In this paper, we study a nonmatching grid finite element approximation of linear elliptic PDEs in the context of the Schwarz alternating domain decomposition.We show that the approximation converges optimally in the maximum norm, on each… (More)
This paper is concerned with the standard finite element approximation of HamiltonJacobi-Bellman Equations (HJB) with nonlinear source terms. Under a realistic condition on the nonlinearity, we characterize the discrete solution as a fixed point of a contraction. As a result of this, we also derive a sharp L∞error estimate of the approximation. Mathematics… (More)
We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The twomeshes beingmutually independent on the overlap… (More)