A Triangular Spectral Element Method Using Fully Tensorial Rational Basis Functions

A rational approximation in a triangle is proposed and analyzed in this paper. The rational basis functions in the triangle are obtained from the polynomials in the reference square through a collapsed coordinate transform. Optimal error estimates for the L2− and H1 0−orthogonal projections are derived with upper bounds expressed in the original coordinates in the triangle. It is shown that the rational approximation is as accurate as the polynomial approximation in the triangle. Illustrative numerical results, which are in agreement with the theoretical estimates, are presented.