An analysis for the compressible Stokes equations by first-order system of least-squares finite element method

2001 ◽  
Vol 17 (6) ◽  
pp. 689-699 ◽  
Author(s):  
Sang Dong Kim ◽  
EunJung Lee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Stokes Equations ◽  
Order System ◽  
First Order ◽  
Element Method

scholarly journals Least-Squares Finite Element Method for a Meso-Scale Model of the Spread of COVID-19

Computation ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 18 ◽  
Author(s):  
Fleurianne Bertrand ◽  
Emilie Pirch
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Scale Model ◽  
Order System ◽  
Time Behavior ◽  
First Order ◽  
Disease Spreading ◽  
Meso Scale ◽  
Element Method

This paper investigates numerical properties of a flux-based finite element method for the discretization of a SEIQRD (susceptible-exposed-infected-quarantined-recovered-deceased) model for the spread of COVID-19. The model is largely based on the SEIRD (susceptible-exposed-infected-recovered-deceased) models developed in recent works, with additional extension by a quarantined compartment of the living population and the resulting first-order system of coupled PDEs is solved by a Least-Squares meso-scale method. We incorporate several data on political measures for the containment of the spread gathered during the course of the year 2020 and develop an indicator that influences the predictions calculated by the method. The numerical experiments conducted show a promising accuracy of predictions of the space-time behavior of the virus compared to the real disease spreading data.

Hybrid First-Order System Least Squares Finite Element Methods with Application to Stokes Equations

2013 ◽  
Vol 51 (4) ◽  
pp. 2214-2237 ◽  
Author(s):  
K. Liu ◽  
T. A. Manteuffel ◽  
S. F. McCormick ◽  
J. W. Ruge ◽  
L. Tang
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Finite Element Methods ◽  
Stokes Equations ◽  
Order System ◽  
First Order

A Least-Squares/Galerkin Finite Element Method for Incompressible Navier-Stokes Equations

2008 ◽  
Author(s):  
Rajeev Kumar ◽  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Basis Functions ◽  
Galerkin Finite Element Method ◽  
Governing Equations ◽  
Galerkin Finite Element ◽  
First Order ◽  
Convection Dominated ◽  
Element Method

The least-squares finite element method (LSFEM), which is based on minimizing the l2-norm of the residual, has many attractive advantages over Galerkin finite element method (GFEM). It is now well established as a proper approach to deal with the convection dominated fluid dynamic equations. The least-squares finite element method has a number of attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike GFEM. However, the higher continuity requirements for second-order terms in the governing equations force the introduction of additional unknowns through the use of an equivalent first-order system of equations or the use of C1 continuous basis functions. These additional unknowns lead to increased memory and computing time requirements that have prevented the application of LSFEM to large-scale practical problems, such as three-dimensional compressible viscous flows. A simple finite element method is proposed that employs a least-squares method for first-order derivatives and a Galerkin method for second order derivatives, thereby avoiding the need for additional unknowns required by pure a LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the leastsquares method. Resulting system matrix is always symmetric and positive definite and can be solved by iterative solvers like pre-conditioned conjugate gradient method. The method is stable for convection-dominated flows and allows for equalorder basis functions for both pressure and velocity. The stability and accuracy of the method are demonstrated with preliminary results of several benchmark problems solved using low-order C0 continuous elements.

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