Fourier Type Super Convergence Study on DDGIC and Symmetric DDG Methods

In this paper, using Fourier analysis technique, we study the super convergence property of the DDGIC (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010 ) and the symmetric DDG (Vidden and Yan in J Comput Math 31(6):638–662, 2013 ) methods for diffusion equation. With k th degree piecewise polynomials applied, the convergence to the solution’s spatial derivative is k th order measured under regular norms. On the other hand when measuring the error in the weak sense or in its moment format, the error is super convergent with ( k + 2 ) th and ( k + 3 ) th orders for its first two moments with even order degree polynomial approximations. We carry out Fourier type (Von Neumann) error analysis and obtain the desired super convergent orders for the case of P 2 quadratic polynomial approximations. The theoretical predicted errors agree well with the numerical results.