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Energy-Corrected Finite Element Methods for Scalar Elliptic Problems [chapter]

Thomas Horger, Markus Huber, Ulrich Rüde, Christia Waluga, Barbara Wohlmuth
2014 Lecture Notes in Computational Science and Engineering  
In this work, we consider the finite element solution of several scalar elliptic problems with singularities in two dimensions.  ...  We outline recent theoretical developments in energy corrected approaches and demonstrate numerically that by local and easy to implement modifications of the discrete operators, optimal convergence orders  ...  Errors 10 × u − u h (γ) 0,α≈0.96475; Convergence analysis of the energy correction method and standard finite element method for the example with 9 singularities.  ... 
doi:10.1007/978-3-319-10705-9_2 fatcat:hnmp5q5szjcjxmdvlsrmcvzriy

Page 6812 of Mathematical Reviews Vol. , Issue 91M [page]

1991 Mathematical Reviews  
(IL-TLAV) Minimum energy triangulations for elliptic problems. Comput. Methods Appl. Mech. Engrg. 84 (1990), no. 3, 257-274.  ...  A minimum energy triangulation, relative to a given elliptic prob- lem, is a triangulation for which the finite element solution has the minimal energy.  ... 

Page 5190 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
finite element methods based on discontinuous approximation spaces for elliptic problems.  ...  Summary: “A posteriori error estimators are derived for linear finite element approximations to elliptic obstacle problems.  ... 

Page 5662 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
Engrg. 97 (1992), no. 3, 399-436; MR 93a:65138], residual and flux projec- tion error estimators for finite element approximations of scalar elliptic problems were reviewed; numerical studies on the per  ...  This paper deals with the problem of obtaining reliable a posteriori error estimators for conforming finite element approximations of weakly coupled elliptic systems.  ... 

Page 3049 of Mathematical Reviews Vol. , Issue 96e [page]

1996 Mathematical Reviews  
Numerical results are presented for the standard displacement finite element method for the scalar equation of or- thotropic heat conduction, for meshes of conforming triangles of degree p, 1 < p <5, and  ...  This analysis is based on the theory of additive subspace correction methods and applies to finite element and pre- wavelet schemes.  ... 

Achieving High-Order Convergence Rates with Deforming Basis Functions

Louis F. Rossi
2005 SIAM Journal on Scientific Computing  
For example, many investigators use Lagrangian methods to approximate passive scalar fields governed by the convection-diffusion equations.  ...  This paper examines a category of high spatial order particle methods using moving, deforming elements to capture passive scalar quantities in a two-dimensional, incompressible fluid flow.  ...  This group has shown that core spreading without refinement or corrections is reasonable for small times, while the corrected method is valid for all finite times [9, 10, 11] .  ... 
doi:10.1137/s1064827503425286 fatcat:ghjp7zanmbc7tflzfonz6qnaqm

Page 2800 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
Summary: “Error estimators are derived using global-local and refined global-local finite element methods and an extrapolation technique.  ...  Summary: “In this paper the generalized difference method of third-order Hermite type for elliptic boundary value problems is discussed.  ... 

Page 6002 of Mathematical Reviews Vol. , Issue 90J [page]

1990 Mathematical Reviews  
To do this with finite elements which were originally designed for scalar fields, that is, nodal elements, is not correct, for such vectorial finite elements have serious drawbacks.  ...  , finite-element methods, and other methods.  ... 

Multiscale finite element coarse spaces for the application to linear elasticity

Marco Buck, Oleg Iliev, Heiko Andrä
2013 Open Mathematics  
., A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 1997, 134(1), 169–189] to the PDE system of linear elasticity.  ...  AbstractWe extend the multiscale finite element method (MsFEM) as formulated by Hou and Wu in [Hou T.Y., Wu X.  ...  Yalchin Efendiev for many fruitful discussions and his valuable comments on the subject of this manuscript.  ... 
doi:10.2478/s11533-012-0166-8 fatcat:gwvujxrky5fehjupdwc3wtodzm

A Study of Suitability and Effectiveness of Various Implementation Options Of Finite Field Arithmetic on Elliptic Curve Crypto System

Bimal Kumar Meher
2009 Journal of clean energy technologies  
A lot of research work is going on in this area since it is suitable for cryptography as well as error correcting codes useful for digital communication, compact disks etc.  ...  In section IX we discuss a few efficient hardware design approaches adopted by many researchers useful for ECC. Index Terms-Finite field, elliptic curve, multiplier, architecture.  ...  Finite Field Multipliers Since the central operation of ECC is the elliptic scalar multiplication (described in section 1), this section gives some more insight into finite field multipliers.  ... 
doi:10.7763/ijcte.2009.v1.61 fatcat:cawhkrdvsfbizceh72d4motbii

Page 4085 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
In 1980, Nédélec proposed a mixed finite-element method for the spatial discretization of Maxwell’s equations in R®; a family of curl- and divergence-conforming finite elements was developed, having the  ...  Summary: “In this paper we discuss convergence of multigrid meth- ods with respect to the maximum norm for 2D elliptic boundary value problems.  ... 

Page 2926 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
He uses the preconditioned conjugate gradient method to solve the symmetric positive definite linear systems which arise from the finite element discretization of the problems.  ...  95e:65093 for both scalar and systems of hyperbolic conservation laws.  ... 

Adaptive finite element methods in computational mechanics

Claes Johnson, Peter Hansbo
1992 Computer Methods in Applied Mechanics and Engineering  
Hansbo, Adaptive finite element methods dependence of IIu -u~,~II on (h, p) is very implicit.  ...  We present a general approach to adaptivity for finite element methods and give applications to linear elasticity, non-linear elasto-plasticity and nonlinear conservation laws, including numerical results  ...  In this paper, we mainly concentrate on elliptic and hyperbolic problems. For a detailed account of adaptive finite element methods for parabolic problems, we refer to [2-51.  ... 
doi:10.1016/0045-7825(92)90020-k fatcat:3qmw7qhamffm3mu74bcc6wluty

On the Design of Small Coarse Spaces for Domain Decomposition Algorithms

Clark R. Dohrmann, Olof B. Widlund
2017 SIAM Journal on Scientific Computing  
An analysis for scalar elliptic and linear elasticity problems reveals that significant reductions in the coarse space dimension can be achieved while not sacrificing the favorable condition number estimates  ...  Numerical examples for problems in three dimensions are presented to illustrate the methods and to confirm the analysis.  ...  This shows that the coarse interpolant belongs to the correct finite element space.  ... 
doi:10.1137/17m1114272 fatcat:mj6vjasvsfbbvjavm4s4gvilse

A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

J. Bakosi, P. Franzese, Z. Boybeyi
2008 Journal of Computational Physics  
All three aspects regarding the grid make use of the finite element method (FEM) employing the simplest linear FEM shape functions.  ...  In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian  ...  This effectively rules out the application of traditional techniques like the finite difference, finite volume or finite element methods for a numerical solution.  ... 
doi:10.1016/j.jcp.2008.02.024 fatcat:aalk5y5kjbcirksoh22sbo5vcm
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