Analysis of iterative methods for the viscous/inviscid coupled problem via a spectral element approximation

Finite difference/spectral approximations for the time-fractional diffusion equation

“…Therefore, at each time step, we obtain a system of linear algebraic equations with different right-hand-side vector fF i g N À1 i¼1 . Since the matrix H is symmetric positive definite, we choose the conjugate gradient method to solve (4.27); see, for example, [22] for some details.…”

Generalized polynomial chaos decomposition and spectral methods for the stochastic Stokes equations

“…We then employ the P N Â P NÀ2 spectral method, as described in (3.4), to discretize this coupling problem. Although the P N Â P NÀ2 approximation of (5.2)-(5.4) can be solved via a direct solver, together with a Uzawa-like technique [9], we choose here to use an iterative method to take advantage of the diagonal dominance of the block matrix S = (s jk ). The method we employ is a kind of block Jacobi iterations [27,33,30] as follows: for k = 0, .…”