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Control‐volume mixed finite element methods
Computational Geosciences, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cai, Z. +3 more
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MIXED FINITE ELEMENT METHODS WITH CONTINUOUS STRESSES
Mathematical Models and Methods in Applied Sciences, 1993We present a modified mixed formulation for second order elliptic equations and linear elasticity problems which automatically satisfies the “ellipticity on the kernel” condition, i.e., one of the two compatibility conditions necessary to ensure stability and optimal error bounds (the other being the Inf-Sup condition).
Brezzi F. +2 more
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On a mixed finite element method for the p-Laplacian
Rocky Mountain Journal of Mathematics, 2000For \(1 < p < \infty \), the quasilinear equation \[ -\nabla \cdot (|\nabla u |^{p-2} \nabla u) = f \quad \text{in }\Omega, \qquad u = 0 \quad \text{on } \Gamma \] is known as the \(p-\)Laplace equation for real \(u\) defined on the two or three-dimensional open set \( \Omega \) which has a Lipschitz boundary \(\Gamma \). (Here \(\nabla u\) denotes the
Farhloul, Mohamed, Manouzi, Hassan
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Mixed finite element methods for the Oseen problem
Numerical Algorithms, 2020In the paper the author reformulates the Oseen problem using tensor gradient of velocity as a new variable. This reduces the initial system of PDEs to a system of the first-order equations. In turn, these relations are rewritten in mixed form using scalar products in Sobolev spaces. It allows to use finite element method with Raviart-Thomas elements to
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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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2013
In this chapter we utilize the Raviart–Thomas spaces to present and analyze specific mixed finite element methods applied to some of the examples studied in Chap. 2. The corresponding discussion follows mainly the presentations in [12, 39, 50, 52].
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In this chapter we utilize the Raviart–Thomas spaces to present and analyze specific mixed finite element methods applied to some of the examples studied in Chap. 2. The corresponding discussion follows mainly the presentations in [12, 39, 50, 52].
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A Mixed Finite Element Method for the Biharmonic Equation
SIAM Journal on Numerical Analysis, 1987We consider the mixed finite element approximation of the biharmonic problem on a smooth domain with either clamped or simply supported boundary conditions. Error estimates are proved for the Ciarlet–Raviart formulation of the clamped plate problem and for a similar method for the simply supported plate problem.
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On Some Mixed Finite Element Methods with Numerical Integration
SIAM Journal on Scientific Computing, 2001In this paper a new family of mixed finite volume methods is analyzed for the approximation of a reaction-diffusion problem. All the methods are obtained starting from the dual mixed formulation of the problem and then employing the lowest-order Raviart--Thomas finite element spaces plus a suitable quadrature formula for the mass matrix.
MICHELETTI, STEFANO +2 more
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Nonconforming Elements in the Mixed Finite Element Method
Journal of Computational Mathematics, 1984In this paper, an abstract error estimate of mixed finite element methods using nonconforming elements is presented. In addition, a class of nonconforming rectangular elements is proposed, and applied to Stokes equations. The optimal error estimate is given.
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Suboptimal and Optimal Convergence in Mixed Finite Element Methods
SIAM Journal on Numerical Analysis, 2002An elliptic partial differential equation may be formulated in different but equivalent ways, and the mixed finite element methods derived from these formulations have different properties. We give general error estimates for two such methods, which are always optimal for the Raviart--Thomas elements, but which are suboptimal for the Brezzi--Douglas ...
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