✦ LIBER ✦

Stable finite element methods with divergence augmentation for the stokes problem

✍ Scribed by K. Kim; S. Lee

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 264 KB
Volume: 14
Category: Article
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00156-7

No coin nor oath required. For personal study only.

✦ Synopsis

The mixed finite element approximation scheme with divergence augmentation for the Stokes problem is analyzed. We show that the Pk+l --Pk-1 triangular elements or the Qk+l -Qk-1 quadrilateral elements in R 2, k > 1, are stable with h k+l/2 convergence in HI-norm for velocity and h k convergence in L2-norm for pressure. Moreover, h k+l convergence in H(div)-norm for velocity can be shown if the domain is convex. In R a, the cross-grid Pk+l -Pk-1 tetrahedral elements, k ~ 2, can be analyzed analogously for the approximation scheme with divergence augmentation and pressure stabilization. A numerical test which confirms the convergence analysis is presented. (~) 2001 Elsevier Science Ltd. All rights reserved.

📜 SIMILAR VOLUMES

Stable and stabilized hp–finite element

Stable and stabilized hp–finite element methods for the Stokes problem

✍ Dominik Schötzau; Klaus Gerdes; Christoph Schwab 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 158 KB

Two hp-finite element methods for the Stokes problem in polygonal domains are presented: We discuss the S k × S k-2 elements which are stable on anisotropic and irregular meshes and introduce a stabilized Galerkin Least Squares approach featuring equal-order interpolation in the velocity and the pre

Finite element methods for the Stokes pr

Finite element methods for the Stokes problem in R3

✍ S. Hong; S. Lee 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 364 KB

## Communicated by F. Brezzi Abstract--We show that the mixed finite element approximation scheme with pressure stabilization for the Stokes problem in R 3 is stable for some tetrahedral elements including the P++I -Pk-1 element and'the cross-grid Pk+l -Pk-1 element, k > 2. (~) 2000 Elsevier Scien

Analysis of strain-pressure finite eleme

Analysis of strain-pressure finite element methods for the Stokes problem

✍ C. Lovadina 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB 👁 2 views

An analysis of some nonconforming approximations of the Stokes problem is presented. The approximations are based on a strain-pressure variational formulation. In particular, a convergence and stability result for a method recently proposed by Bathe and Pantuso is provided.

conforming finite element methods for th

conforming finite element methods for the coupled Stokes and Darcy problem

✍ Yumei Chen; Feiteng Huang; Xiaoping Xie 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 300 KB

This paper proposes and analyzes a numerical method for solving the coupled Stokes and Darcy problem, an interface problem between a fluid, governed by Stokes equations, and a flow in a porous medium, governed by Darcy equations. The method employs H(div) conforming finite elements for the velocity

Locking, spurious mechanisms, and pressu

Locking, spurious mechanisms, and pressure divergence in penalty finite element methods for Stokes flow problems

✍ K.C. Park 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 1024 KB

The quadrilateral ‘Mini’ finite element

The quadrilateral ‘Mini’ finite element for the Stokes problem

✍ Wen Bai 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 466 KB

We propose two mixed finite element methods for the Stokes equations in two space dimensions. Starting from a Q,-Q, combination for the velocity and pressure, it is studied how to introduce internal degrees of freedom into the velocity space in order to obtain a LBB-stable combination. The LBB stabi