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Page 498 of Mathematical Reviews Vol. , Issue 2002A [page]

2002 Mathematical Reviews  
A posteriori estimates are proved for the gradient of the solution to a second-order elliptic problem approximated by the finite element method.  ...  (PRC-BAP; Kowloon); Han, Weimin (1-IA; Lowa City, IA); Huang, Hong-ci (PRC-BAP; Kowloon Some mixed finite element methods for biharmonic equation.  ... 

Page 443 of Mathematical Reviews Vol. , Issue 89A [page]

1989 Mathematical Reviews  
Summary: “We present a multilevel algorithm for the mixed finite element approximation of the Stokes problem by the mini-element. A local L?  ...  The author gives a direct method for solving the discrete mixed finite element equations of the biharmonic problem with homo- geneous boundary values.  ... 

Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

Rakhim Aitbayev
2006 Numerical Methods for Partial Differential Equations  
Efficient multilevel preconditioners are developed and analyzed for the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem.  ...  The quadrature scheme is formulated using the Bogner-Fox-Schmit rectangular element and the product two-point Gaussian quadrature.  ...  Multilevel preconditioners for the finite element Galerkin solution of the biharmonic problem (1.2) using conforming and nonconforming rectangular elements are studied in [5] .  ... 
doi:10.1002/num.20122 fatcat:3kjfvcg47bazngdn5dptexcodq

Page 5571 of Mathematical Reviews Vol. , Issue 96i [page]

1996 Mathematical Reviews  
The multilevel finite-element method for solving the biharmonic equation. (Russian. English and Russian summaries) Vestnik S.-Peterburg. Univ. Mat. Mekh. Astronom. 1993, vyp. 3, 144-145, 153 (1994).  ...  Summary: “We consider adaptive multilevel methods for the non- conforming P1 finite element approximation of linear second- order, elliptic boundary value problems.  ... 

Page 1412 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Os- wald has adapted these methods for discretizations of the fourth- order biharmonic problem by rectangular conforming Bogner- Fox-Schmit elements and non-conforming Adini elements and has derived optimal  ...  Summary: “In recent years multilevel preconditioners such as BPX have become more and more popular for solving second-order elliptic finite element discretizations by iterative methods. P.  ... 

Multilevel Filtering Preconditioners: Extensions to More General Elliptic Problems

Charles H. Tong, Tony F. Chan, C. C. Jay Kuo
1992 SIAM Journal on Scientific and Statistical Computing  
It is then shown how to effectively apply this concept to other elliptic problems such as the second-order anisotropic problem, biharmonic equation, equations on locally refined grids and interface operators  ...  The concept of multilevel filtering (MF) preconditioning applied to second-order selfadjoint elliptic problems is briefly reviewed.  ...  We can borrow the finite element analysis result from them and we would expect the MGMF precon-ditioners to be effective also for meshes with local refinement.  ... 
doi:10.1137/0913012 fatcat:3zfis62vrza73jkvpxm4ijaicu

A comparison of a posteriori error estimates for biharmonic problems solved by the FEM

Karel Segeth
2012 Journal of Computational and Applied Mathematics  
In the paper, we are concerned with a review and comparison of error estimation procedures for the biharmonic and some more general fourth order partial differential problems with special regards to the  ...  MSC: 65N15 65N30 Keywords: Biharmonic equation hp-adaptive finite element method A posteriori error estimates a b s t r a c t The classical a posteriori error estimates are mostly oriented to the use in  ...  supported by the Ministry of Education, Youth, and Sports of the Czech Republic.  ... 
doi:10.1016/ fatcat:jlz7uwudlbeqdn4u4yfxapttba

Recent advances and trends in numerical techniques for process simulation

W. Joppich, S. Mijalković
1997 Microelectronics and reliability  
The major task and obstacles for each of these numerical segments are recognized, and some recently proposed techniques to circumvent current limitations, as well as possible directions for future research  ...  In this paper, an outlook on the current status and trends in numerical techniques for efficient multidimensional bulk process simulation is given.  ...  The special emphasis is put on multilevel adaptive methods associated with the multigrid solving procedures.  ... 
doi:10.1016/s0026-2714(97)00005-x fatcat:gh5ciya3bre3nmnlh6c6tb3kqu

Semi-Analytical Finite Strip Transfer Matrix Method for Buckling Analysis of Rectangular Thin Plates

Li-Ke Yao, Bin He, Yu Zhang, Wei Zhou
2015 Mathematical Problems in Engineering  
A new approach, namely semi-analytical Finite Strip Transfer Matrix Method, is developed for the buckling analysis of plates.  ...  In this investigation, rectangular thin plates with loaded edges simply supported can be discretized by semi-analytical finite strip technology.  ...  Acknowledgment The research is financed by National Key Science Foundation Program (51624001), Natural Science Foundation of Jiangsu Province, China (BK20130911).  ... 
doi:10.1155/2015/485686 fatcat:gjf7vdrhjvcrpf22z6c4tr3vra

A review of some a posteriori error estimates for adaptive finite element methods

Karel Segeth
2010 Mathematics and Computers in Simulation  
We present a brief review of some error estimation procedures for some particular both linear and nonlinear differential problems with special regards to the needs of the hp-method.  ...  Recently, the adaptive finite element methods have gained a very important position among numerical procedures for solving ordinary as well as partial differential equations arising from various technical  ...  Acknowledgments This research was partly supported by the Ministry of Education, Youth, and Sports of the Czech Republic through Research Center 1M4674788502, by the Grant Agency of the Academy of Sciences  ... 
doi:10.1016/j.matcom.2008.12.019 fatcat:q26wvfhzfvg2tg3sz2luod6p6q

Isogeometric Schwarz preconditioners for the biharmonic problem

D. Cho, L. F. Pavarino, S. Scacchi
2018 Electronic Transactions on Numerical Analysis  
The proposed preconditioner is based on solving local biharmonic problems on overlapping subdomains that form a partition of the CAD domain of the problem and on solving an additional coarse biharmonic  ...  problem associated with the subdomain coarse mesh.  ...  parallel local biharmonic problems on each Ω i and a coarse biharmonic problem on a coarse mesh associated with the subdomain partition of Ω.  ... 
doi:10.1553/etna_vol49s81 fatcat:5ie4k2dngjdrzdfiv7ayhv2vha

A mixed finite element formulation for the boundary controllability of the wave equation

R. Glowinski, W. Kinton, M. F. Wheeler
1989 International Journal for Numerical Methods in Engineering  
Acknowledgement The authors would like to thank Cray Research for providing the computer time required to obtain these calculations.  ...  mixed finite element method.  ...  For further details, we refer you to [4] . The second section of the paper describes the mixed finite element method along with the approximating spaces used in the procedure.  ... 
doi:10.1002/nme.1620270313 fatcat:bhs6mmgmfjbojo5j2j23z32hr4

Optimality of multilevel preconditioning for nonconforming P1 finite elements

P. Oswald
2008 Numerische Mathematik  
We prove the optimality of hierarchical and BPX-type preconditioners for finite element discretizations with nonconforming P1 finite elements.  ...  The main new tool is an improved Bernstein type inequality for an associated subdivision process generated by the prolongations which allows us to give an asymptotically optimal upper bound for the spectrum  ...  with one or two smoothing steps for nonconforming finite element (FE) discretizations given their components, even in the case of model problems such as Laplace's equation on polygonal domains.  ... 
doi:10.1007/s00211-008-0182-6 fatcat:xbi5ny766jcsdbxlf335qgetmi

Fast Numerical Methods for Non-local Operators

Wolfgang Hackbusch, Stefan Sauter, Christoph Schwab
2004 Oberwolfach Reports  
Steinbach's talk Tearing and Interconnecting Domain Decomposition Methods, the FETI/BETI method was considered which is an efficient preconditioned iterative solver for finite element/boundary element  ...  With growing demand for reliable discretisation methods for such applications the need of fast numerical methods for non-local operators has increased rapidly worldwide since the mid 80th and we list below  ...  and sparse tensor products of multilevel finite element spaces are analyzed and implemented.  ... 
doi:10.4171/owr/2004/33 fatcat:y2fti3akzrbrxjf7i3h7nnv7oa

The mathematics of finite elements and applications

1989 International Journal of Engineering Science  
C JOHNSON Adaptive finite element methods in compti ational mechanics We give an overview of our recent work on adaptive finite element methods for problems in solid and fluid mechanics including elasticity  ...  M J CROCHET Finite elements for potymer flow. A comparison Over the last five years, several finite element methods have been introduced for analyzing viscoelastic flow.  ...  For the biharmonic equation, two problems with a boundary singularity were also solved, the determination of the Airy stress-function for a rectangular elastic plate containing an edge crack under uniform  ... 
doi:10.1016/0020-7225(89)90012-8 fatcat:z6hknn325re4tbssbqqzmcketa
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