We consider the iterative solution of linear systems arising from four convection–diffusion model problems: scalar convection–diffusion problem, Stokes problem, Oseen problem and Navier–Stokes problem. We design preconditioners for these model problems that are based on Kronecker product approximations (KPAs). For this we first identify explicit Kronecker product structure of the coefficient ma...

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• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...

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This paper deals with the numerical solution of a scalar nonlinear convection–diffusion equation. The space semi–discretization is carried out by the discontinuous Galerkin finite element method. Several possibilities of the time discretizations are discussed. To obtain a stable and efficient schemes we use implicit scheme for linear terms in combination with suitable explicit scheme for nonlin...

The main purpose of this paper is to analyze the stability and error estimates of the local discontinuous Galerkin (LDG) methods coupled with carefully chosen implicit-explicit (IMEX) Runge-Kutta time discretization up to third order accuracy, for solving one-dimensional linear convection-diffusion equations. In the time discretization the convection term is treated explicitly and the diffusion...

Integration factor (IF) methods are a class of efficient time discretization methods for solving stiff problems via evaluation of an exponential function of the corresponding matrix for the stiff operator. The computational challenge in applying the methods for partial differential equations (PDEs) on high spatial dimensions (multidimensional PDEs) is how to deal with the matrix exponential for...

We study the existence and uniqueness of solutions of the convective-diffusive elliptic equation −div(D∇u) + div(V u) = f posed in a bounded domain Ω ⊂ RN , with pure Neumann boundary conditions D∇u · n = (V · n)u on ∂Ω. Under the assumption that V ∈ Lp(Ω)N with p = N if N ≥ 3 (resp. p > 2 if N = 2), we prove that the problem has a solution u ∈ H1(Ω) if ∫ Ω f dx = 0, and also that the kernel is...

An analytic and empirical study of line iterative methods for solving the discrete convection-diffusion equation is performed. The methodology consists of performing one step of the cyclic reduction method, followed by iteration on the resulting reduced system using line orderings of the reduced grid. Two classes of iterative methods are considered: block stationary methods, such as the block G...