Viscosity robust weak Galerkin finite element methods for Stokes problems
نویسندگان
چکیده
<p style='text-indent:20px;'>In this paper, we develop a viscosity robust weak Galerkin finite element scheme for Stokes equations. The major idea achieving pressure-independent energy-error estimate is to use divergence preserving velocity reconstruction operator in the discretization of right hand side body force. optimal convergence results and pressure have been established paper. Finally, numerical examples are presented validating theoretical conclusions.</p>
منابع مشابه
Robust Globally Divergence-free Weak Galerkin Methods for Stokes Equations
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 boundar...
متن کاملA Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems
A residual type a posteriori error estimator is presented and analyzed for Weak Galerkin finite element methods for second order elliptic problems. The error estimator is proved to be efficient and reliable through two estimates, one from below and the other from above, in terms of an H1-equivalent norm for the exact error. Two numerical experiments are conducted to demonstrate the effectivenes...
متن کاملWeak Galerkin Finite Element Methods on Polytopal Meshes
This paper introduces a new weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite element partitions of arbitrary polytopes with certain shape regularity. The paper explains how the numerical schemes are designed ...
متن کاملDiscontinuous Galerkin finite element methods for second order hyperbolic problems
In this paper, we prove a priori and a posteriori error estimates for a finite element method for linear second order hyperbolic problems (linear wave equations) based on using spacetime finite element discretizations (for displacements and displacement velocities) with (bilinear) basis functions which are continuous in space and discontinuous in time. We refer to methods of this form as discon...
متن کاملA weak Galerkin finite element method for the Navier-Stokes equations
In this paper, a weak Galerkin finite element method (WGFEM) is proposed for solving the Navier-Stokes equations (NSEs). The existence and uniqueness of the WGFEM solution of NSEs are established. The WGFEM provides very accurate numerical approximations for both the velocity field and pressure field, even with very high Reynolds numbers. The salient feature is that the flexibility of the WGFEM...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic research archive
سال: 2021
ISSN: ['2688-1594']
DOI: https://doi.org/10.3934/era.2020096