Use of Mixed Cubature Rule for Evaluation of Integrals over Triangular Region in Adaptive Environment

Abstract

A new mixed cubature rule is established for 2-simplexes (i.e., triangles). Extending anti-Gauss 3-point rule and Fejer’s second 3-point rule in two dimensions and then combining those the mixed cubature rule is formed which is of precision 5. Also an adaptive cubature algorithm is devised to boost up the mixed cubature rule. Some test integrals are also numerically evaluated to show the efficiency of the mixed rule in adaptive environment.