We compute low-cardinality algebraic cubature formulas on convex or concave polygonal elements with a circular edge, by subdivision into circular quadrangles, blending formulas via subperiodic trigonometric Gaussian quadrature and final compression via Caratheodory–Tchakaloff subsampling of discrete measures. We also discuss applications to the VEM (Virtual Element Method) in computational mechanics problems.
Algebraic cubature on polygonal elements with a circular edge
Sommariva, A.;Vianello, M.
2020
Abstract
We compute low-cardinality algebraic cubature formulas on convex or concave polygonal elements with a circular edge, by subdivision into circular quadrangles, blending formulas via subperiodic trigonometric Gaussian quadrature and final compression via Caratheodory–Tchakaloff subsampling of discrete measures. We also discuss applications to the VEM (Virtual Element Method) in computational mechanics problems.
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