An approximation scheme for variational inequalities with convex and coercive Hamiltonians

Shuo Huang

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arXiv · 1810.08842

An approximation scheme for variational inequalities with convex and coercive Hamiltonians

Shuo Huang

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Abstract

We propose an approximation scheme for a class of semilinear variational inequalities whose Hamiltonian is convex and coercive. The proposed scheme is a natural extension of a previous splitting scheme proposed by Liang, Zariphopoulou and the author for semilinear parabolic PDEs. We establish the convergence of the scheme and determine the convergence rate by obtaining its error bounds. The bounds are obtained by Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation, in which a key step is to introduce a variant switching system.

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Shuo Huang. 2018-10-20. An approximation scheme for variational inequalities with convex and coercive Hamiltonians. https://arxiv.org/abs/1810.08842

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