scholarly journals A locally conservative, discontinuous least-squares finite element method for the Stokes equations

2011 ◽  
Vol 68 (6) ◽  
pp. 782-804 ◽  
Author(s):  
Pavel Bochev ◽  
James Lai ◽  
Luke Olson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Stokes Equations ◽  
Locally Conservative ◽  
Element Method

A Least-Squares Galerkin Split Finite Element Method for Compressible Navier-Stokes Equations

2009 ◽  
Author(s):  
Rajeev Kumar ◽  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Compressible Flows ◽  
Stokes Equations ◽  
Least Squares Method ◽  
Iterative Solvers ◽  
Benchmark Problems ◽  
System Matrix ◽  
Element Method

A novel 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 a pure LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the least-squares 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 equal-order basis functions for both pressure and velocity. The stability and accuracy of the method are demonstrated in the context of compressible flows by results of few compressible benchmark problems solved using low-order C0 continuous elements.

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