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CIRP Encyclopedia of Production Engineering, 2019
0 v dx, ∀v ∈ H̊([0, 1]). The interval [0, 1] is divided into 3N equispaced cells (where N is a positive integer). After forming a P1 C finite element space VN , the error ‖u−uh‖H1 is found not to converge to zero. Explain why this is expected? 5. (a) Let
Steve Rotenberg
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0 v dx, ∀v ∈ H̊([0, 1]). The interval [0, 1] is divided into 3N equispaced cells (where N is a positive integer). After forming a P1 C finite element space VN , the error ‖u−uh‖H1 is found not to converge to zero. Explain why this is expected? 5. (a) Let
Steve Rotenberg
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Aging, Shaking, and Cracking of Infrastructures, 2021
Victor E. Saouma +1 more
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Victor E. Saouma +1 more
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Springer Series in Solid and Structural Mechanics, 2017
Friedel Hartmann, Peter Jahn
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Friedel Hartmann, Peter Jahn
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Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis, 1995
Finite elements with support on two intervals span the space of piecewise polynomials with degree 2n-1 and n-1 continuous derivatives. Function values and n-1 derivatives at each mesh-point determine these "Hermite finite elements". The n basis functions satisfy a dilation equation with n by n matrix coefficients. Orthogonal to this scaling subspace is
V. Strela, G. Strang
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Finite elements with support on two intervals span the space of piecewise polynomials with degree 2n-1 and n-1 continuous derivatives. Function values and n-1 derivatives at each mesh-point determine these "Hermite finite elements". The n basis functions satisfy a dilation equation with n by n matrix coefficients. Orthogonal to this scaling subspace is
V. Strela, G. Strang
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2007
This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter
Marc Hoit, Gary Consolazio
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This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter
Marc Hoit, Gary Consolazio
+4 more sources
Preconditioning Complicated Finite Elements by Simple Finite Elements
SIAM Journal on Scientific Computing, 1996A very subtle and useful method of preconditioning finite elements with a large number of degrees of freedom by simpler finite elements is proposed. A second-order problem (Laplace equation) and a fourth-order problem (biharmonic equation) are considered as examples.
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2002
The finite-difference approach with equidistant grids is easy to understand and straightforward to implement. The resulting uniform rectangular grids are comfortable, but in many applications not flexible enough. Steep gradients of the solution require a finer grid such that the difference quotients provide good approximations of the differentials.
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The finite-difference approach with equidistant grids is easy to understand and straightforward to implement. The resulting uniform rectangular grids are comfortable, but in many applications not flexible enough. Steep gradients of the solution require a finer grid such that the difference quotients provide good approximations of the differentials.
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Computational Homogenization of Heterogeneous Materials with Finite Elements
Solid Mechanics and its Applications, 2020J. Yvonnet
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