Strang G, Fix GJ. An Analysis of the Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1973. Home/Search Document Not in Database Summary Related Articles Check |
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.... surfaces (section 4) and we know the discrete minimal surfaces as well (section 3) so we can check that the ab ove procedure produces good approximations for the eigenvalues and smooth eigenfunctions (section 7) which indeed mustb e the case,b y the theory of the finite element method [4] [8]. With these successful tests, we go on to consider cases where we do not apriori know what the smooth eigenfunctions shouldb e, such as the Jorge Meeks 3 noid and the genus 1 Costa surface (section 7) We note that the ab ove procedure can alsob e implemented using discrete approximating surfaces ....
....the second half of the introduction. If a sequence of compact cmc discrete surfaces T # i=1 converges (in the Sob olev H norm as graphs over the limiting surface) to a smooth compact cmc surface #:M# , then standard estimates from the theory of finite elements (see, for example, 4] or [8]) imply that the eigenvalues and eigenvectors (piece wise linearly extended to functions) of the operators L h of the j converge to the eigenvalues and eigenfunctions of theJacob i operator L of # (convergence is in the L for the eigenfunctions) ....
G. Fix and G. Strang. An analysis of the finite element method. Prentice-Hall, 1973.
Computation of Optical Modes inside - Axisymmetric Open Cavity (Correct)
....to the geometrical discretisation of the domain. The two concentric semi discs that are used to model the cavity are approximated by regular triangular meshes. Consequently, their perimeter are discretised as polygons which reduces the approximation power of the quadratic elements. Strang and Fix [31] state that the convergence rate should be O(h ) We observed a strong reduction of the convergence rate to almost linear, see Table 4.2. We believe that we can rectify this problem by introducing curvilinear elements. 13 Fig. 8. Comparison of rst and second order element functions. The ....
G. Strang and G. J. Fix. An Analysis of the Finite Element Method. Wellesley{ Cambridge Press, Wellesley, MA, 1973.
Numerical Methods for Accurate Finite Element Solutions of.. - Kim, Lee, Oh (2002) (Correct)
....smooth. Singularities can therefore arise when ## or some part of the data are not smooth. In the theory and practice of FEM, a considerable e#ort has been made to design special approaches to deal with problems containing singularities. The most typical approaches are Mesh Refinement ( 5] 13] [22], 26] Use of special elements ( 1] 2] 23] 27] and Use of the Enriched(nonlocal) basis functions ( 8] 15] 22] Recently, Babuska Oh introduced a new method, called the method of Auxiliary Mapping(MAM) to deal with the corner singularity( 4] The essence of this method involves locally ....
....of FEM, a considerable e#ort has been made to design special approaches to deal with problems containing singularities. The most typical approaches are Mesh Refinement ( 5] 13] 22] 26] Use of special elements ( 1] 2] 23] 27] and Use of the Enriched(nonlocal) basis functions ( 8] 15] [22]) Recently, Babuska Oh introduced a new method, called the method of Auxiliary Mapping(MAM) to deal with the corner singularity( 4] The essence of this method involves locally transforming a region around each singularity to a new domain by use of a conformal mapping such as # = z . Here ....
Strang, G. and Fix, G.: An Analysis of the Finite Element Method, Prentice-Hall, 1973.
Implicit Method for the Computation of Unsteady Flows.. - Venkatakrishnan.. (1995) (6 citations) (Correct)
....the mass matrix entries by computing the average of this polynomial over the control volume. The mass matrix M couples the system of ODE s in Eqn. 3) The effect is that even with an explicit scheme, one has to deal with the solution of a coupled linear system. A technique called mass lumping [38], replaces the matrix M by the identity matrix. For second order accurate cell centered schemes, which employ the triangles as the control volumes and store the values at the centroids, mass lumping does not compromise the accuracy, since the point value at the centroid matches the average value ....
....whereas the spatial differencing employed here is upwind biased. After experimenting with a oneparameter family of mass matrices, we have found that the lumped mass matrix gives the lowest errors with this particular spatial discretization. It is well known in finite element literature [38] that in some cases the lumping of the mass matrix does not compromise the solution accuracy, but that the mass matrix may play a crucial role when higher order discretizations are considered. To examine this, we employ a quadratic reconstruction procedure utilizing point values. With h i = x i ....
G. Strang and G. J. Fix, An analysis of the finite element method, Prentice Hall, New Jersey, 1973.
L'Approximation Filaire En Régime Harmonique - Becache (1999) (Correct)
.... equations int egrales (cf x3.4.1 pour l equation int egrale compl ete) on distingue deux cas suivant que les segments sont adjacents ou confondus. Dans le premier cas (segments disjoints) il n y a pas de singularit e et on peut utiliser des formules de quadratures (formule de Gauss Legendre, [1, 39, 40]) pour approcher les int egrales. En pratique, on a int eret a utiliser un nombre de points de quadrature qui d epend de la distance entre les segments consid er e. Mazari propose d utiliser une formule a N i points sur K i , avec N i = max(2; E( d ij ) o u d ij = 1 j(z i Gamma1 z i ) ....
G. Strang and G. J. Fix. An analysis of the finite element method. Englewood Cliffs Prentice Hall, 1973. 27
New Estimates For Ritz Vectors - Knyazev (1997) (4 citations) (Correct)
.... corresponding orthogonal projectors Q strongly converge to the identity operator, then Q)A Q#, in fact even Q)A#, tends to zero [5] Such a situation is typical for the Rayleigh Ritz method applied for approximation of low eigenpairs of differential operators, e.g. using finite elements [16], 3] However, if the operator A is not compact, then Q)A Q# is not necessarily small, even for Q strongly converging to the identity [6] The importance of Q)A Q# is based on the representation A = QA Q (I Q) I Q) and the fact that Q)# Q)A Q# = QA(I ....
G. Strang and G. Fix. An Analysis of the Finite Element Method. Prentice-Hall, 1973. MR 56:1747
A Least Squares Coupling Method with Finite Elements and.. - Maischak, Stephan Self-citation (Fix) (Correct)
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G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Series in Automatic Computation, Prentice-Hall, 1973.
International Journal For Numerical Methods In Engineering - Int Numer Meth (Correct)
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Strang G, Fix GJ. An Analysis of the Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1973.
Explicit A Posteriori Error Estimates for Eigenvalue.. - Walsh, Reese, Hetmaniuk (2005) (Correct)
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Strang, G. & Fix, G. J. (1973). An analysis of the finite element method. Prentice-Hall.
Spectral Partitioning Works:Planar graphs and finite element.. - Spielman, Teng (1996) (34 citations) (Correct)
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G. Strang and G. J. Fix. An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
B-Spline Approximation Of Neumann - Problems Klaus Ollig (Correct)
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G. Strang and G.J. Fix. An Analysis of the Finite Element Method. PrenticeHall 1973.
Regularization Methods In The Numerical Analysis Of Some Degenerate .. - Pop (1998) (Correct)
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G. Strang & G. Fix,, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
On the Foundations of Computational Mathematics - Baxter, Iserles (2002) (Correct)
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G. Strang and G. Fix. An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, NJ, 1973. 31
Adjoint Error Correction for Integral Outputs - Giles, Pierce (Correct)
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G. Strang and G. Fix. An Analysis of the Finite Element Method. PrenticeHall, 1973.
A Robust and Efficient Numerical Method for Nonlinear Protein.. - Holst (1994) (Correct)
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G. Strang and G. Fix, An analysis of the finite element method, Prentice-Hall, Englewood Cli#s, NJ, 1973.
From Finite Differences to Finite Elements - A short history of.. - Thomee (1999) (Correct)
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G. Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ, 1973.
Unknown - Omega Gamma Norm (Correct)
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Strang, G. and Fix, G.J. An Analysis of the Finite Element Method. Prentice-Hall, 1973.
Numerical Solution of the Nonlinear Poisson-Boltzmann.. - Holst, Saied (1995) (1 citation) (Correct)
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G. Strang and G. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cli#s, NJ, 1973.
A Modified Finite Volume Approximation of Second-Order.. - Ewing, Iliev, Lazarov (2001) (Correct)
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G. Strang and G. Fix, An analysis of finite element methods, Prentice-Hall Inc, N.J., 1980.
Journal of Computational Physics 176, 40--69 (2002) - Doi Jcph Available (Correct)
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G. Strang and G. J. Fix, An Analysis of the Finite Element Method (Wellesley--Cambridge Press, Wellesley, MA, 1988).
Quality Meshing with Weighted Delaunay Refinement - Siu-Wing Cheng Tamal (2002) (4 citations) (Correct)
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G. Strang and G. J. Fix. An Analysis of the Finite Element Method. Prentice Hall, 1973.
Scattered Data Interpolation Methods for - Electronic Imaging Systems (Correct)
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G. Strang and G. J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ #1973#.
Adjoint Error Correction for Integral Outputs - Giles, Pierce (Correct)
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G. Strang and G. Fix. An Analysis of the Finite Element Method. Prentice-Hall, 1973.
Linear Operators and Transfer Equations in Global Illumination - Arvo (Correct)
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Gilbert Strang and George J. Fix. An Analysis of the Finite Element Method. Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
Appendix A - Discretisation Integral Equations (Correct)
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G. Strang and G.J. Fix. An Analysis of the Finite Element Method. Prentice Hall, Inc., 1973.
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