High degree efficient symmetrical Gaussian quadrature rules for the triangle

Abstract

Abstract Gaussian quadrature is required for the computation of matrices based on the isoparametric formulztion of the finite element method. A brief review of existing quadrature rules for the triangle is given, and the method for the determination of high degree efficient symmetrical rules for the triangle is discussed. New quadrature rules of degree 12–20 are presented, and a short FORTRAN program is included.