Abstract
This paper deals with the approximation of solutions to a degenerate variational inequality of parabolic type with a non-smooth final condition arising from American option pricing by the piecewise linear finite element method in space and an implicit time-stepping scheme. We show that the error of the approximation in a weighted Sobolev norm is of order 𝒪(h 2/3+Δ t 1/3) under some realistic regularity assumptions on the exact solution, where h and Δ t denote the mesh parameters in space and time, respectively. Numerical examples are presented to confirm our theoretical results.
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