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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 concerned with the standard finite element approximation of Hamilton-Jacobi-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.
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)
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