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Stability and error analysis of mixed finite volume methods for advectivediffusive problems
 Comput. Math. Appl
"... We consider a convection–diffusion–reaction problem, and we analyze a stabilized mixed finite volume scheme introduced in [23]. The scheme is presented in the format of Discontinuous Galerkin methods, and error bounds are given, proving O(h1/2) convergence in the L2norm for the scalar variable, wh ..."
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We consider a convection–diffusion–reaction problem, and we analyze a stabilized mixed finite volume scheme introduced in [23]. The scheme is presented in the format of Discontinuous Galerkin methods, and error bounds are given, proving O(h1/2) convergence in the L2norm for the scalar variable, which is approximated with piecewise constant elements. 1
CrouzeixRaviart and RaviartThomas Elements for Acoustic . . .
, 2003
"... We consider the eigenvalue problem arising from small vibration uid{structure interaction. We propose using the lowest order Raviart{Thomas (RT) element for the linear uid and the rst order nonconforming Crouzeix{Raviart (CR) element for the linear elastic structure. The RT element, whose unkno ..."
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We consider the eigenvalue problem arising from small vibration uid{structure interaction. We propose using the lowest order Raviart{Thomas (RT) element for the linear uid and the rst order nonconforming Crouzeix{Raviart (CR) element for the linear elastic structure. The RT element, whose unknowns are the normal projection of the eld variable on the element sides, are known to give solutions free from spurious nonzero frequency circulation modes The unknowns on the CR element are chosen as the normal and tangential projection of the eld variable at each side node. This choice leads to that the normal degrees of freedom on the interface will be the same for the structure and the uid as long as the meshes match on the interface. Further, a consistent stabilizing term is added to the weak form to make the CR element stable for elasticity. An additional bene t of the CR element is that is does not lock for near incompressible materials.
A Mathematical Analysis For Numerical Well
, 2001
"... In this paper, we discuss some numerical well models for nonDarcy ows in porous media. Basically, the numerical well models are derived based upon some simple mathematical calculations using the various approximation techniques associated with the various grid con gurations. The mathematical an ..."
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In this paper, we discuss some numerical well models for nonDarcy ows in porous media. Basically, the numerical well models are derived based upon some simple mathematical calculations using the various approximation techniques associated with the various grid con gurations. The mathematical analysis given here is simple, direct, and systematic.