Abstract
The Schwarz method for a class of elliptic variational inequalities with noncoercive operator was studied in this work. The author proved the error estimate in L∞-norm for two domains with overlapping nonmatching grids using the geometrical convergence of solutions and the uniform convergence of subsolutions.
Highlights
More than one hundred years ago, Schwarz algorithms were proposed for proving the solvability of PDEs on a complicated domain
We give a new approach to the finite element approximation for the problem of variational inequality with noncoercive operator
The proof stands on a Lipschitz continuous dependency with respect to the source term for variational inequality, while in [5] the proof stands on a Lipschitz continuous dependency with respect to the boundary condition
Summary
More than one hundred years ago, Schwarz algorithms were proposed for proving the solvability of PDEs on a complicated domain. With parallel calculators, this rediscovery of these methods as algorithms of calculations was based on a modern variational approach. We give a new approach to the finite element approximation for the problem of variational inequality with noncoercive operator. This problem arises in stochastic control (see [10]).
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