Results 221 to 230 of about 28,597 (266)
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2003
This chapter explains the need for mixed finite element methods and the algorithmic ingredients of this discretization approach. Various Diffpack tools for easy programming of mixed methods on unstructured grids in 2D and 3D are described. As model problems for exemplifying the formulation and implementation of mixed finite elements we address the ...
K.-A. Mardal, H. P. Langtangen
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This chapter explains the need for mixed finite element methods and the algorithmic ingredients of this discretization approach. Various Diffpack tools for easy programming of mixed methods on unstructured grids in 2D and 3D are described. As model problems for exemplifying the formulation and implementation of mixed finite elements we address the ...
K.-A. Mardal, H. P. Langtangen
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Applied Mathematics and Computation, 2013
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Qing Yang 0030, Yirang Yuan
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Qing Yang 0030, Yirang Yuan
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Mixed finite element approximation
2021This chapter is concerned with the approximation of the model problem analyzed in the previous chapter. We focus on the Galerkin approximation in the conforming setting. We establish necessary and sufficient conditions for well-posedness, and we derive error bounds in terms of the best-approximation error.
Alexandre Ern, Jean-Luc Guermond
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A New Superconvergence for Mixed Finite Element Approximations
SIAM Journal on Numerical Analysis, 2002A new superconvergence result is established for numerical solutions of elliptic problems obtained from the mixed finite element method of Raviart--Thomas over rectangular partitions. The well-known optimal order error estimate in L 2 -norm for the flux approximation is of order ${\cal O}(h ...
Richard E. Ewing +2 more
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Conforming Rectangular Mixed Finite Elements for Elasticity
Journal of Scientific Computing, 2010A family of rectangular mixed finite elements for the stress-displacement system of the phase elasticity problem is described in the paper. Estimates of a certain type on the convergence velocity are found. In the reviewer's opinion the estimates in the paper (see Theorems 2 and 3) are not of an interest neither from the numerical point of view nor ...
Shao-Chun Chen, Ya-Na Wang
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A nonstandard mixed finite element family
Numerische Mathematik, 2009The mixed method for the Poisson equation is applied to finite element functions with some extra continuity conditions in the BDM space or BDDF space. The degrees of freedom on the interfaces are adapted. Error estimates are given in terms of the \(L_2\) norm for \(\sigma\) and a broken \(H^1\) norm for \(u\), i.e., not for the pair \(H(\text{div ...
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Mixed methods and the marriage between “mixed” finite elements and boundary elements
Numerical Methods for Partial Differential Equations, 1991AbstractWhen fields that describe a physical situation extend over the whole space, but with complex behavior (nonlinearity, coupling, etc.) only in a bounded region and simple behavior in the rest of space, it may be worthwhile to treat the inner field by a finite elements procedure and the outer field by boundary elements.
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A Mixed Finite Element Method for Coupled Plates
Computational Methods in Applied MathematicsAbstract This paper introduces a mixed finite element method for the problem of two coupled plates with mixed boundary conditions and rigid junction conditions. By introducing the union of stresses and moments as an independent variable, which is of significant interest in practical applications, a mixed formulation is developed and its ...
Jun Hu 0013 +3 more
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Numerische Mathematik, 1980
We present here some new families of non conforming finite elements in ?3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
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We present here some new families of non conforming finite elements in ?3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
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A mixed finite element for the stokes problem using quadrilateral elements
Advances in Computational Mathematics, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohamed Farhloul, Michel Fortin
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