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2014
Finite element method (FEM) is widely used in various engineering fields to solve problems with too many complexities to be dealt with by certain conventional approaches. In 1943, Courant proposed the theoretical basis of the method, and, in 1956, Turner et al.
Toru Otsuru +3 more
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Finite element method (FEM) is widely used in various engineering fields to solve problems with too many complexities to be dealt with by certain conventional approaches. In 1943, Courant proposed the theoretical basis of the method, and, in 1956, Turner et al.
Toru Otsuru +3 more
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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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1999
If the fluid flow domain and boundary conditions are well posed then the Navier-Stokes equations can be analytically solved, however this, is possible only for the simplest type of problems.
Hou-Cheng Huang +2 more
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If the fluid flow domain and boundary conditions are well posed then the Navier-Stokes equations can be analytically solved, however this, is possible only for the simplest type of problems.
Hou-Cheng Huang +2 more
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2007
Abstract In this chapter, we present the method of finite elements which is the numerical method of choice for the calculation of solutions of elliptic boundary value problems, but is also used for parabolic or hyperbolic problems as we shall see.
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Abstract In this chapter, we present the method of finite elements which is the numerical method of choice for the calculation of solutions of elliptic boundary value problems, but is also used for parabolic or hyperbolic problems as we shall see.
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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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2016
Coupling Mortar Finite Element and Boundary Element Methods for 2D Navier-Stokes Equations Courant Element: Before and After Iterative Methods for Solving Stiff Elliptic Problems Straight and Curved Finite Elements of Class C1 and Some Applications to Thin Shell Problems Exact Controllability to Solve the Helmholtz Equation with Absorbing Boundary ...
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Coupling Mortar Finite Element and Boundary Element Methods for 2D Navier-Stokes Equations Courant Element: Before and After Iterative Methods for Solving Stiff Elliptic Problems Straight and Curved Finite Elements of Class C1 and Some Applications to Thin Shell Problems Exact Controllability to Solve the Helmholtz Equation with Absorbing Boundary ...
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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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2018
In this chapter, we first introduce the differences between the finite element method (FEM) and the previously introduced FDM and FVM. Then, the focus will be placed on the Galerkin method for obtaining the weak form of the governing equation. Using thermomechanics as an example, the discretization of the weak form of the governing equations with ...
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In this chapter, we first introduce the differences between the finite element method (FEM) and the previously introduced FDM and FVM. Then, the focus will be placed on the Galerkin method for obtaining the weak form of the governing equation. Using thermomechanics as an example, the discretization of the weak form of the governing equations with ...
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2011
Finite element methods (FEM) were used very early for problems in structural mechanics. Such problems often have a natural discretization by partitioning the structure in a number of finite elements, and this gave the name to this class of methods. This kind of mechanical approach merged with the more mathematical approach that gained momentum in the ...
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Finite element methods (FEM) were used very early for problems in structural mechanics. Such problems often have a natural discretization by partitioning the structure in a number of finite elements, and this gave the name to this class of methods. This kind of mechanical approach merged with the more mathematical approach that gained momentum in the ...
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2012
Wir haben die Methode der finiten Elemente schon in Kapitel 3.7 zum Losen gewohnlicher Randwertprobleme eingefuhrt und angewandt. Das eigentliche Anwendungsgebiet sind jedoch die partiellen Differenzialgleichungen und vorzugsweise die elliptischen Randwertprobleme.
Claus-Dieter Munz, Thomas Westermann
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Wir haben die Methode der finiten Elemente schon in Kapitel 3.7 zum Losen gewohnlicher Randwertprobleme eingefuhrt und angewandt. Das eigentliche Anwendungsgebiet sind jedoch die partiellen Differenzialgleichungen und vorzugsweise die elliptischen Randwertprobleme.
Claus-Dieter Munz, Thomas Westermann
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