Some High Degree Gauss Legendre Quadrature Formulas For Triangles

The finite element method is one of the most powerful computational techniques for approximate solution of a variety of "real world" engineering and applied science problems for over half a century since its inception in the mid 1960. Today, finite element analysis (FEA) has becomes an integral and major component in the design or modeling of a physical phenomenon in various disciplines. The triangular and quadrilateral elements with either straight sides or curved sides are very widely used in a variety of applications. The basic problem of integrating a function of two variables over the surface of the triangle is the subject of extensive research by many authors and the precision of these formulas is limited to degree 20 at most. Derivation of high precision formulas is now possible over the triangular region by application product formulas based only on the sampling points and weights of the well known Gauss Legendre quadrature rules.