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

2014
*
Lecture Notes in Computational Science and Engineering
*

In this work, we consider the

doi:10.1007/978-3-319-10705-9_2
fatcat:hnmp5q5szjcjxmdvlsrmcvzriy
*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. ...##
###
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

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] . ...

##
###
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

2013
*
Open Mathematics
*

., A multiscale

doi:10.2478/s11533-012-0166-8
fatcat:gwvujxrky5fehjupdwc3wtodzm
*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. ...##
###
A Study of Suitability and Effectiveness of Various Implementation Options Of Finite Field Arithmetic on Elliptic Curve Crypto System

2009
*
Journal of clean energy technologies
*

A lot of research work is going on in this area since it is suitable

doi:10.7763/ijcte.2009.v1.61
fatcat:cawhkrdvsfbizceh72d4motbii
*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. ...##
###
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

1992
*
Computer Methods in Applied Mechanics and Engineering
*

Hansbo, Adaptive

doi:10.1016/0045-7825(92)90020-k
fatcat:3qmw7qhamffm3mu74bcc6wluty
*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. ...##
###
On the Design of Small Coarse Spaces for Domain Decomposition Algorithms

2017
*
SIAM Journal on Scientific Computing
*

An analysis

doi:10.1137/17m1114272
fatcat:mj6vjasvsfbbvjavm4s4gvilse
*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. ...##
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A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

2008
*
Journal of Computational Physics
*

All three aspects regarding the grid make use of the

doi:10.1016/j.jcp.2008.02.024
fatcat:aalk5y5kjbcirksoh22sbo5vcm
*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. ...
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