Randomized, one-point-per-triangle quadrature assembles finite element systems for rough-coefficient elliptic equations with proven first-order convergence, and an importance-sampling variant reaches nearly second order for smooth data.
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Application of Randomized Quadrature Formulas to the Finite Element Method for Elliptic Equations
Randomized, one-point-per-triangle quadrature assembles finite element systems for rough-coefficient elliptic equations with proven first-order convergence, and an importance-sampling variant reaches nearly second order for smooth data.