Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Navier–Stokes Equations01:28

Navier–Stokes Equations

2.9K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.9K
Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

4.2K
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
4.2K
Stokes' Law01:20

Stokes' Law

3.4K
Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
3.4K
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

1.9K
An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
1.9K
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

1.0K
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
1.0K
Mesh Analysis01:20

Mesh Analysis

1.8K
Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
1.8K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Numerical Investigation of the Effect of Unsteadiness on Three-Dimensional Flow of an Oldroyb-B Fluid.

PloS one·2015
Same author

On a cubically convergent iterative method for matrix sign.

TheScientificWorldJournal·2015
Same author

On a derivative-free variant of king's family with memory.

TheScientificWorldJournal·2015
Same author

Geometric construction of eighth-order optimal families of Ostrowski's method.

TheScientificWorldJournal·2015
Same author

On a new three-step class of methods and its acceleration for nonlinear equations.

TheScientificWorldJournal·2014
Same author

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

TheScientificWorldJournal·2014

Related Experiment Video

Updated: Apr 13, 2026

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery
06:18

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Published on: December 6, 2024

1.2K

The mixed finite element multigrid method for stokes equations.

K Muzhinji1, S Shateyi1, S S Motsa2

  • 1Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa.

Thescientificworldjournal
|May 7, 2015
PubMed
Summary

This study compares iterative solvers for Stokes problems, finding Braess-Sarazin smoothers significantly improve geometric multigrid performance for solving symmetric indefinite systems.

More Related Videos

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

4.7K
Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology
08:54

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

Published on: April 18, 2018

10.2K

Related Experiment Videos

Last Updated: Apr 13, 2026

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery
06:18

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Published on: December 6, 2024

1.2K
Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression
13:07

Optical Coherence Tomography Based Biomechanical Fluid-Structure Interaction Analysis of Coronary Atherosclerosis Progression

Published on: January 15, 2022

4.7K
Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology
08:54

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

Published on: April 18, 2018

10.2K

Area of Science:

  • Numerical Analysis
  • Computational Fluid Dynamics

Background:

  • Finite element discretization of the Stokes problem yields symmetric indefinite linear systems.
  • Efficient iterative solvers are crucial for these systems.

Purpose of the Study:

  • Investigate the geometric multigrid solver for solving indefinite systems.
  • Compare the performance of different smoothing strategies within the multigrid method.

Main Methods:

  • Applied geometric multigrid solver with distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin smoothers.
  • Utilized a two-dimensional domain with Hood-Taylor Q2-Q1 finite rectangular elements.
  • Derived theoretical convergence results.

Main Results:

  • Braess-Sarazin smoothers demonstrated superior performance in the geometric multigrid solver.
  • Numerical results confirmed the efficiency and robustness of the multigrid method.
  • Theoretical convergence results were validated.

Conclusions:

  • Geometric multigrid with Braess-Sarazin smoothers is an effective method for solving Stokes problems.
  • The study confirms the efficiency and robustness of this approach for symmetric indefinite systems.