Robust Globally Divergence-free Weak Galerkin Methods for Stokes Equations
نویسندگان
چکیده
This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the Pk/Pk−1 (k ≥ 1) discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise Pl/Pk (l = k − 1, k) for the trace approximations of the velocity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods. Mathematics subject classification: 65M60, 65N30.
منابع مشابه
Hybridized globally divergence-free LDG methods. Part I: The Stokes problem
We devise and analyze a new local discontinuous Galerkin (LDG) method for the Stokes equations of incompressible fluid flow. This optimally convergent method is obtained by using an LDG method to discretize a vorticity-velocity formulation of the Stokes equations and by applying a new hybridization to the resulting discretization. One of the main features of the hybridized method is that it pro...
متن کاملHigh order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows
In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency of the discretization method is the disctinction between stiff linear parts and less stiff non-linear parts with respect to their temporal and spatial treatm...
متن کاملA Wavelet { Galerkin Algorithm
In this paper we derive an algorithm for solving the Stokes{equations for the example of the Driven{Cavity{Problem. We treat the Stokes{equations in the divergence{free weak formulation and show the construction of divergence{free reenable functions, which will be used as trial functions in the Galerkin{method. The system will be solved by means of the preconditioned cg{method. We make use of m...
متن کاملA radial basis Galerkin method for spherical surface Stokes equations
Constructing efficient algorithms to simulate the Stokes and NavierStokes equations (NSEs) with divergence-free constraint on spherical surfaces plays a major role in many climate models on the global scale. Compactly supported radial basis functions (with centers at well distributed mesh points on spherical surfaces) are efficient tools for computing divergence-free numerical solutions for par...
متن کاملA Note on Discontinuous Galerkin Divergence-free Solutions of the Navier-Stokes Equations
We present a class of discontinuous Galerkin methods for the incompressible Navier-Stokes equations yielding exactly divergence-free solutions. Exact incompressibility is achieved by using divergence-conforming velocity spaces for the approximation of the velocities. The resulting methods are locally conservative, energy-stable, and optimally convergent. We present a set of numerical tests that...
متن کامل