A Lobatto interpolation grid over the triangle

^** Email: m.blyth{at}uea.ac.uk^*** Email: cpozrikidis{at}ucsd.edu A sequence of increasingly refined interpolation grids overthe triangle is proposed, with the goal of achieving uniformconvergence and ensuring high interpolation accuracy. The numberof interpolation nodes, N, corresponds to a complete mth-orderpolynomial expansion with respect to the triangle barycentriccoordinates, which arises by the horizontal truncation of thePascal triangle. The proposed grid is generated by deployingLobatto interpolation nodes along the three edges of the triangle,and then computing interior nodes by averaged intersectionsto achieve three-fold rotational symmetry. Numerical computationsshow that the Lebesgue constant and interpolation accuracy ofthe proposed grid compares favorably with those of the best-knowngrids consisting of the Fekete points. Integration weights correspondingto the set of Lobatto triangle base points are tabulated.