Higher-order temporal integration for the incompressible Navier–Stokes equations in bounded domains

Modified augmented Lagrangian preconditioners for the incompressible NavierStokes equations

We study different variants of the augmented Lagrangian (AL)-based block-triangular preconditioner introduced by the first two authors in [SIAM J. Sci. Comput. 2006; 28: 2095–2113]. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual method (GMRES) applied to various finite element and Marker-and-Cell discretizations of the Oseen problem in two and thr...

Higher Order Cauchy Problems in Bounded Domains

Abstract. We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Baeumer, Meerschaert and Nane [10] and Meerschaert, Nane and Vellaisamy [31], and Nane [36]. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0 < β...

Lattice Boltzmann Model for the Incompressible NavierStokes Equation

In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...

On Higher Order Finite Element Discretizations for the Incompressible Navier-stokes Equations in Three Dimensions

Domains for Higher-Order Games

We study two-player inclusion games played over word-generating higher-order recursion schemes. While inclusion checks are known to capture verification problems, two-player games generalize this relationship to program synthesis. In such games, non-terminals of the grammar are controlled by opposing players. The goal of the existential player is to avoid producing a word that lies outside of a...