Mixed and Hybrid Finite Element Methods

By Franco Brezzi, Michel Fortin. Springer Series in Computational Mathematics, 2011

4,130 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/ff847b07f42ab3314d915dfc71a5c75dbfc0ee60

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In Computational Mechanics

In Mechanics of Materials

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Citations in the corpus

Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow (2002, methodology): “Moreover, by using the Piola transform, one can include tri- or bilinearly distorted rectangular parallelepipeds [ 12 ,30].”
A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier (2000, background): “3, is a consequence of the approximation property on Xh, the continuity of the bilinear form b(·, ·), and an inf-sup condition [13].”
Divergence free Virtual Elements for the Stokes problem on polygonal meshes (2015, background): “It is well-known (see for instance [26]) that given • a polynomial function gb ∈ [Bk(∂K)], • a polynomial function h ∈ Gk−2(K), • a polynomial function g ∈ Pk−1(K) satisfying the compatibility condition ∫”
Discrete Hodge-Operators: an Algebraic Perspective - Abstract (2001, methodology): “[ 17 ]). Hitherto unknown problems arise from hybrid eliminations.”
Mixed finite element methods for linear elasticity with weakly imposed symmetry (2007, positive): “c(kωk + kµk), while kdσk = kµk, and thus we have the desired bound (7.2). We have thus veriﬁed the stability conditions (A1) and (A2), and so may apply the standard theory of mixed methods (cf. [12], [13], [17], [20]) and standard results about approximation by ﬁnite element spaces to obtain converg”
An energy‐consistent material‐point method for dynamic finite deformation plasticity (2006, background): “Unfortunately, the four-node constant pressure/volume quadrilateral (Q1/P0) finite element does not satisfy the inf-sup(LBB) condition [13].”
The GLT class as a generalized Fourier analysis and applications (2006, methodology): “, [20,24]) by using hat functions, leads to a sequence of Hermitian positive definite matrices {An} which is distributed as k(x, s) over ̃ ×Qd (see [7]), where”
A parallel domain decomposition method for coupling of surface and groundwater flows (2009, background): “The coupled system (1)–(4) has the following weak formulation which yields a unique solution based on Brezzi’s theory [ 1 ].”
Discontinuous Galerkin approximation of two-phase flows in heterogeneous porous media with discontinuous capillary pressures (2010, background): “(32) These conditions fully prescribe the degrees of freedom of the vector field u h [9].”