The figure presents: (a) The problem domain and boundary conditions, and (b), a plot of the dual problem right-hand side function.

The figure presents: (a) The problem domain and boundary conditions, and (b), a plot of the dual problem right-hand side function.

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We present an adaptive multilevel Monte Carlo (AMLMC) algorithm for approximating deterministic, real-valued, bounded linear functionals that depend on the solution of a linear elliptic PDE with a lognormal diffusivity coefficient and geometric singularities in bounded domains of $\mathbb{R}^d$. Our AMLMC algorithm is built on the results of the we...