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A Multiscale Finite-Element-Method
Civil-Comp Proceedings, 1997Abstract This paper describes a hierarchical overlay of a p -version finite element approximation on a coarse mesh and an h -approximation on a geometrically independent fine mesh. The length scales of the local problem may be some orders of magnitude below the scale of the global problem.
Rank, E., Krause, R.
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Curved Elements in the Finite Element Method. II
SIAM Journal on Numerical Analysis, 1973Curved elements, introduced by the author in [13] and [14], which are suitable for solving boundary value problems of the second order in plane domains with an arbitrary boundary are discussed. An approximation theorem is proved, the Dirichlet problem for a ${\mathop W\limits^{\circ}} _2^{(1)} $-elliptic equation is considered as a model problem and ...
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An Introduction to Finite Element Methods
Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, 2015The most common techniques for obtaining numerical solutions to partial differential equations on non-trivial domains are (high order) finite element methods. The given domain is subdivided into simple geometric objects and an approximate solution is computed as a linear combination of locally supported basis functions.
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SIAM Review, 1976
The purpose of this paper is to show how Lagrange multipliers can be used with finite elements to achieve a number of desirable properties in the underlying approximation. For elliptic boundary value problems, variational principles can be developed in which all boundary conditions are natural.
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The purpose of this paper is to show how Lagrange multipliers can be used with finite elements to achieve a number of desirable properties in the underlying approximation. For elliptic boundary value problems, variational principles can be developed in which all boundary conditions are natural.
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Nonconforming Elements in the Finite Element Method with Penalty
SIAM Journal on Numerical Analysis, 1973Summary: A penalty method approach is used for achieving convergence of a finite element method using nonconforming elements. Error estimates are given.
Babuška, Ivo, Zlámal, Milos
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The construction of large element in finite element method
Applied Mathematics and Mechanics, 1983In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.
Liang, Guo-ping, Fu, Zi-zhi
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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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An Intrinsically Parallel Finite Element Method
Journal of Scientific Computing, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Susanne C. Brenner +3 more
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1991
The approximate methods presented at the end of the preceding chapter for the solution of the vibration problems of continuous systems are based on the assumption that the shape of the deformation of the continuous system can be described by a set of assumed functions. By using this approach, the vibration of the continuous system which has an infinite
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The approximate methods presented at the end of the preceding chapter for the solution of the vibration problems of continuous systems are based on the assumption that the shape of the deformation of the continuous system can be described by a set of assumed functions. By using this approach, the vibration of the continuous system which has an infinite
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Introduction to the finite element method
2017 IEEE International Symposium on Electromagnetic Compatibility & Signal/Power Integrity (EMCSI), 2017A brief presentation on how to solve using the finite element method and the application of the method to microstrip problem are discussed.
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