Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A least-squares approach based on a discrete minus one inner product for first order systems
Mathematics of Computation
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II
SIAM Journal on Numerical Analysis
Multilevel First-Order System Least Squares for Elliptic Grid Generation
SIAM Journal on Numerical Analysis
Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations
SIAM Journal on Numerical Analysis
First-order system least squares (FOSLS) for coupled fluid-elastic problems
Journal of Computational Physics
Quadrilateral H(div) Finite Elements
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
On a composite implicit time integration procedure for nonlinear dynamics
Computers and Structures
Benchmark problems for incompressible fluid flows with structural interactions
Computers and Structures
Journal of Computational Physics
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In this exploratory article a new least squares formulation for the solution of fluid structure interaction problems consisting of the Navier-Stokes equations and the equations of linear elastodynamics will be analysed. It is an extension of the ideas presented in [Cai Z, Starke G. First-order system least squares for the stress-displacement formulation: linear elasticity. SIAM J Numer Anal 2003;41:715-30, Cai Z, Lee B, Wang P. Least-squares methods for incompressible newtonian fluid flow: linear stationary problem. SIAM J Numer Anal 2004;42(2):843-59] for the equations of linear elasticity and the Stokes equations. In those papers a mixed first order least squares formulation which includes the stresses as additional unknowns is proposed. As the stress field has to be approximated by discrete subspaces of H"d"i"v, the usual compatibility of the normal traction will automatically be satisfied on any element edge. Therefore the strongly coupled problem can be formulated in an almost uniform manner. After introducing the basic ideas and the general formulation, a computational error analysis is presented which confirms optimal convergence rates in all problem unknowns. Then the formulation is applied to test cases which come closer to real life applications. Also for these cases the formulation achieves a convincing accuracy.