A survey of numerical cubature over triangles. (English) Zbl 0820.41026

Gautschi, Walter (ed.), Mathematics of computation, 1943-1993: a half- century of computational mathematics. Mathematics of computation 50th anniversary symposium, August 9-13, 1993, Vancouver, Canada. Providence, RI: American Mathematical Society. Proc. Symp. Appl. Math. 48, 127-150 (1994).
Summary: This survey collects together theoretical results in the area of numerical cubature over triangles and is a vehicle for a current bibliography. We treat first the theory relating to regular integrands and then the corresponding theory for singular integrands with emphasis on the “full corner singularity”. Within these two sections we treat successively approaches based on transforming the triangle into a square, formulas based on polynomial moment fitting, and extrapolation techniques. Within each category we quote key theoretical results without proof, and relate other results and references to these. Nearly all the references we have found may be readily placed in one of these categories. This survey is theoretical in character and does not include recent work in adaptive and automatic integration.
For the entire collection see [Zbl 0807.00006].


41A55 Approximate quadratures
41A63 Multidimensional problems
65B15 Euler-Maclaurin formula in numerical analysis
65D32 Numerical quadrature and cubature formulas