LEAST SQUARES FINITE ELEMENT SOLUTION OF COMPRESSIBLE AND INCOMPRESSIBLE FLOWS
- 1 February 1992
- journal article
- Published by Emerald Publishing in International Journal of Numerical Methods for Heat & Fluid Flow
- Vol. 2 (2) , 99-113
- https://doi.org/10.1108/eb017483
Abstract
We investigate the application of a least squares finite element method for the solution of fluid flow problems. The least squares finite element method is based on the minimization of the L2 norm of the equation residuals. Upon discretization, the formulation results in a symmetric, positive definite matrix system which enables efficient iterative solvers to be used. The other motivations behind the development of least squares finite element methods are the applicability of higher order elements and the possibility of using the norm associated to the least squares functional for error estimation. For steady incompressible flows, we develop a method employing linear and quadratic triangular elements and compare their respective accuracy. For steady compressible flows, an implicit conservative least squares scheme which can capture shocks without the addition of artificial viscosity is proposed. A refinement strategy based upon the use of the least squares residuals is developed and several numerical examples are used to illustrate the capabilities of the method when implemented on unstructured triangular meshes.Keywords
This publication has 14 references indexed in Scilit:
- Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equationsPublished by Elsevier ,2003
- Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady euler equationsInternational Journal for Numerical Methods in Fluids, 1989
- A stable least‐squares finite element method for non‐linear hyperbolic problemsInternational Journal for Numerical Methods in Fluids, 1988
- Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier‐Stokes equationsInternational Journal for Numerical Methods in Fluids, 1987
- A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolationsComputer Methods in Applied Mechanics and Engineering, 1986
- A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamicsComputer Methods in Applied Mechanics and Engineering, 1986
- A robust incomplete Choleski‐conjugate gradient algorithmInternational Journal for Numerical Methods in Engineering, 1984
- The incomplete Cholesky—conjugate gradient method for the iterative solution of systems of linear equationsJournal of Computational Physics, 1978
- The finite element method with Lagrangian multipliersNumerische Mathematik, 1973
- Several Strategies for Reducing the Bandwidth of MatricesPublished by Springer Nature ,1972