Polynomial approximation constitutes a fundamental framework in numerical analysis and applied mathematics, where complex functions are represented by simpler polynomial forms. A central pillar of ...

Mathematics of Computation, Vol. 81, No. 278 (APRIL 2012), pp. 861-877 (17 pages) The problem of the rate of convergence of Legendre approximation is considered. We first establish the decay rates of ...

We present a finite difference scheme, applicable to general irregular planar domains, to approximate the biharmonic equation. The irregular domain is embedded in a Cartesian grid. In order to ...