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This article provides a survey of recent research efforts on the applicationof quasi-Monte Carlo (QMC) methods to elliptic partial differential equations(PDEs) with random diffusion coefficients. It considers, and contrasts, theuniform case versus the lognormal case, single-level algorithms versusmulti-level algorithms, first order QMC rules versus higher order QMC rules,and deterministic QMC methods versus randomized QMC methods. It gives a summaryof the error analysis and proof techniques in a unified view, and provides apractical guide to the software for constructing and generating QMC pointstailored to the PDE problems. The analysis for the uniform case can begeneralized to cover a range of affine parametric operator equations.

Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients - a survey of analysis and implementation