Abstract
Many attempts have been made in the past to regain the spectral accuracy
of the spectral methods, which is lost drastically due to the presence
of discontinuity. In this article, an attempt has been made to show that
mollification using Legendre and Chebyshev polynomial based kernels
improves the convergence rate of the Fourier spectral method. Numerical
illustrations are provided with examples involving one or more
discontinuities and compared with the existing Dirichlet kernel
mollifier. Dependence of the efficiency of the polynomial mollifiers on
the parameter P is analogous to that in the Dirichlet mollifier,
which is detailed by analysing the numerical solution. Further, they are
extended to linear scalar conservation law problems.