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Elliptic Boundary Value Problem
Mixed Finite Element
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Error estimators for a mixed method
Multigrid methods in science and engineering
Superconvergence and a posteriori error estimation fortriangular mixed finite elements
A posteriori error estimate for the mixed finite element method
A Posteriori Err...
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Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems
Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems,Ronald H. w. Hoppe,Barbara Wohlmuth
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Adaptive Multilevel Techniques for Mixed Finite Element Discretizations of Elliptic Boundary Value Problems
(
Citations: 16
)
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Ronald H. w. Hoppe
,
Barbara Wohlmuth
We consider
mixed finite element
discretizations of linear secondorder elliptic boundary value problems with respect to an adaptivelygenerated hierarchy of possibly highly nonuniform simplicial triangulations.By a well known postprocessing technique the discrete problem isequivalent to a modified nonconforming discretization which is solved bypreconditioned cgiterations using a multilevel BPXtype preconditionerdesigned for standard nonconforming approximations. Local refinementof the...
Published in 1994.
Cumulative
Annual
Citation Context
(5)
...Other a posteriori error estimators for the mixed finite element methods can be found at [25, 62,
43
, 39, 44, 45]...
Long Chen
,
et al.
Convergence and optimality of adaptive mixed finite element methods
...We refer to [5] for algorithmic details and MATLAB routines and to [2, 10, 18,
13
] for empirical examples...
...The disadvantage is the possibly slow convergence of the Uzawa algorithm relative to multilevel solver [
13
]...
CARSTEN CARSTENSEN
,
et al.
ERROR REDUCTION AND CONVERGENCE FOR AN ADAPTIVE MIXED FINITE ELEMENT M...
...Previous works on error estimation for mixed finite element methods on conforming grids include [11, 12, 17,
24
, 39, 25]...
...Estimators based on superconvergence error estimates are developed in [12,
24
]...
Mary F. Wheeler
,
et al.
A Posteriori Error Estimates for the Mortar Mixed Finite Element Metho...
...For mixed finite element methods involving RaviartThomas éléments we refer to [1,25,26,42,
44
,45]...
RUDI BECK
,
et al.
RESIDUAL BASED A POSTERIORI ERROR ESTIMATORS FOR EDDY CURRENT COMPUTAT...
...A posteriori error estimates for mixed finite element methods were started in the works of Alonso [7], Braess and Verf¨urth [15], Carstensen [23], Hoppe and Wohlmuth [
39
], Achchab et al. [2], Wohlmuth and Hoppe [67], Carstensen and Bartels [24], Kirby [42], El Alaoui and Ern [34], Wheeler and Yotov [66], and Lovadina and Stenberg [44]...
MARTIN VOHRALIK
.
UNIFIED PRIMAL FORMULATIONBASED A PRIORI AND A POSTERIORI ERROR ANALY...
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(
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Published in 1992.
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Citations
(16)
Convergence and optimality of adaptive mixed finite element methods
(
Citations: 10
)
Long Chen
,
Michael J. Holst
,
Jinchao Xu
Journal:
Mathematics of Computation  Math. Comput.
, vol. 78, no. 265, pp. 3553, 2009
Numerical simulation of piezoelectrically agitated surface acoustic waves on microfluidic biochips
(
Citations: 10
)
Andreas Gantner
,
Ronald H. W. Hoppe
,
Daniel Köster
,
Kunibert Siebert
,
Achim Wixforth
Journal:
Computing and Visualization in Science
, vol. 10, no. 3, pp. 145161, 2007
Functional approach to a posteriori error estimation for elliptic optimal control problems with distributed control
A. Gaevskaya
,
R. H. W. Hoppe
,
S. Repin
Journal:
Journal of Mathematical Sciences
, vol. 144, no. 6, pp. 45354547, 2007
ERROR REDUCTION AND CONVERGENCE FOR AN ADAPTIVE MIXED FINITE ELEMENT METHOD
(
Citations: 26
)
CARSTEN CARSTENSEN
,
R. H. W. HOPPE
Journal:
Mathematics of Computation  Math. Comput.
, 2005
A Posteriori Error Estimates for the Mortar Mixed Finite Element Method
(
Citations: 13
)
Mary F. Wheeler
,
Ivan Yotov
Journal:
Siam Journal on Numerical Analysis  SIAM J NUMER ANAL
, vol. 43, no. 3, pp. 10211042, 2005