The mortar finite element method for Bingham fluids
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 35, Issue: 1, page 153-164
- ISSN: 0764-583X
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topHild, Patrick. "The mortar finite element method for Bingham fluids." ESAIM: Mathematical Modelling and Numerical Analysis 35.1 (2010): 153-164. <http://eudml.org/doc/197575>.
@article{Hild2010,
abstract = {
This paper deals with the flow problem of a
viscous plastic fluid in a cylindrical pipe. In order to
approximate this problem governed by a variational inequality, we
apply the nonconforming
mortar finite element method. By using
appropriate techniques, we are able to prove the convergence of the method
and to obtain the same convergence rate as in the conforming case.
},
author = {Hild, Patrick},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Viscoplastic fluid; Bingham model; variational inequality;
mortar finite element method; a priori error estimates.; Bingham fluid; viscoplastic fluid; cylindrical pipe; nonconforming mortar finite element method; convergence rate},
language = {eng},
month = {3},
number = {1},
pages = {153-164},
publisher = {EDP Sciences},
title = {The mortar finite element method for Bingham fluids},
url = {http://eudml.org/doc/197575},
volume = {35},
year = {2010},
}
TY - JOUR
AU - Hild, Patrick
TI - The mortar finite element method for Bingham fluids
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 153
EP - 164
AB -
This paper deals with the flow problem of a
viscous plastic fluid in a cylindrical pipe. In order to
approximate this problem governed by a variational inequality, we
apply the nonconforming
mortar finite element method. By using
appropriate techniques, we are able to prove the convergence of the method
and to obtain the same convergence rate as in the conforming case.
LA - eng
KW - Viscoplastic fluid; Bingham model; variational inequality;
mortar finite element method; a priori error estimates.; Bingham fluid; viscoplastic fluid; cylindrical pipe; nonconforming mortar finite element method; convergence rate
UR - http://eudml.org/doc/197575
ER -
References
top- Y. Achdou and O. Pironneau, A fast solver for Navier-Stokes equations in the laminar regime using mortar finite elements and boundary element methods. SIAM J. Numer. Anal.32 (1995) 985-1016.
- R.A. Adams, Sobolev Spaces. Academic Press, New York (1975).
- F. Ben Belgacem, The mixed mortar finite element method for the incompressible Stokes problem: Convergence analysis. SIAM J. Numer. Anal.37 (2000) 1085-1100.
- F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Numer. Math.84 (1999) 173-197.
- F. Ben Belgacem, P. Hild and P. Laborde, Extension of the mortar finite element method to a variational inequality modeling unilateral contact. Math. Models Methods Appl. Sci.9 (1999) 287-303.
- C. Bernardi, N. Debit and Y. Maday, Coupling finite element and spectral methods: First results. Math. Comp.54 (1990) 21-39.
- C. Bernardi and V. Girault, A Local regularisation operator for triangular and quadrilateral finite elements. SIAM J. Numer. Anal.35 (1998) 1893-1916.
- C. Bernardi, Y. Maday and A.T. Patera, A new nonconforming approach to domain decomposition: the mortar element method, in Collège de France Seminar, H. Brezis and J.-L. Lions Eds., Pitman (1994) 13-51.
- P.E. Bjrstad and O.B. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal.23 (1986) 1097-1120.
- H. Brezis, Monotonicity in Hilbert spaces and some applications to nonlinear partial differential equations, in Contributions to nonlinear functional analysis, E. Zarantonello Ed., Academic Press, New York (1971) 101-156.
- P.-G. Ciarlet, The finite element method for elliptic problems, in Handbook of numerical analysis, Vol. II, Part 1, P.-G. Ciarlet and J.-L. Lions Eds., North Holland, Amsterdam (1991) 17-352.
- N. Debit, La méthode des éléments avec joints dans le cas du couplage de méthodes spectrales et méthodes d'éléments finis: résolution des équations de Navier-Stokes. Ph.D. thesis, University of Paris VI, France (1991).
- G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972).
- R.S. Falk, Error estimates for the approximation of a class of variational inequalities. Math. Comp.28 (1974) 963-971.
- R. Glowinski, Lectures on numerical methods for non-linear variational problems. Springer, Berlin (1980).
- P. Hild, Problèmes de contact unilatéral et maillages éléments finis incompatibles. Ph.D. thesis, University of Toulouse III, France (1998).
- J.-L. Lions and G. Stampacchia, Variational inequalities. Comm. Pure. Appl. Math.XX (1967) 493-519.
- P.P. Mosolov and V.P. Miasnikov, Variational methods in the theory of the fluidity of a viscous-plastic medium. PPM, J. Mech. Appl. Math.29 (1965) 545-577.
- P.P. Mosolov and V.P. Miasnikov, On stagnant flow regions of a viscous-plastic medium in pipes. PPM, J. Mech. Appl. Math.30 (1966) 841-854.
- P.P. Mosolov and V.P. Miasnikov, On qualitative singularities of the flow of a viscoplastic medium in pipes. PPM, J. Mech Appl. Math.31 (1967) 609-613.
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