A spectral deferred correction method for incompressible flow with variable viscosity

Spectral Deferred Correction Method

φ(t) = F (t, φ(t)), t ∈ [a, b], φ(a) = φa. (1.1) where φa, φ(t) ∈ C n and F : R × C → C. Let {t}n=0 be equally spaced nodes in the interval [a, b] with t0 = a, tN = b. Let {t j n} M j=0 be the Legendre-Gauss-Lobatto nodes in the subinterval [tn, tn+1] with t 0 n = tn, t M n = tn+1. Denote ∆n = t j+1 n − t j n. 1.1 Forward Euler Scheme The Picard integral equation in each [tn, tn+1] associated w...

A multi-level spectral deferred correction method

The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels...

A Spectral Deferred Correction Method for Solving Cardiac Models

A Spectral Deferred Correction Method for Solving Cardiac Models

A Least Squares Spectral Element Method for Incompressible Flow Simulations

Convergence theory for spectral deferred correction

In a recent article [2] Dutt, Greengard and Rohklin define two newmethods of deferred correction. Convergence for the the first method, using one step methods, has been proven in Hansen [8]. In this paper we augment the theory presented in [8] and use this to prove convergence for the second deferred correction method in [2] using linear k-step methods. This method has been known as Spectral De...