Mixed finite element methods for elliptic problems

By Douglas N. Arnold. 1990

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Citations in the corpus

Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data (2019, methodology): “Following the Hellinger-Reissner principle [49], the mixed variational principle states that the solution (τ ∗, u∗) of the Darcy flow problem is the unique critical point of the functional”
Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, methodology): “In [2,31], a stabilized Lagrange space is designed to satisfy the Ladyzhenskaya–Babuska–Brezzi (LBB) condition [1,14], the basic idea being to reduce the number of Lagrange multipliers by certain rules.”
MIXED FINITE ELEMENT METHODS: IMPLEMENTATION WITH ONE UNKNOWN PER ELEMENT, LOCAL FLUX EXPRESSIONS, POSITIVITY, POLYGONAL MESHES, AND RELATIONS TO OTHER METHODS (2013, background): “, [39]), multiscale and mortar versions (see, e.”
A BDDC ALGORITHM FOR A MIXED FORMULATION OF FLOW IN POROUS MEDIA (2005, methodology): “A BNN version of the Method II of [9] was proposed in [3], see also [20].”
A novel alpha finite element method (αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements (2008, background): “So far, the mixed FEM models [16–19] based on the mixed variational principles focus mainly to improve the accuracy of the solution.”
Families of 4-node and 9-node finite elements for a finite deformation shell theory. An assesment of hybrid stress, hybrid strain and enhanced strain elements (2000, methodology): “Basic features of the shell theory itself are: (1) The incorporation of seven degrees of freedom in the formulation. ( 2 ) Thickness change is included.”
A Multiscale Mortar Mixed Finite Element Method (2007, methodology): “A substructuring domain decomposition algorithm based on an algorithm of Glowinski and Wheeler [27] can be used to solve the linear system of equations resulting from (2.”
A novel FEM by scaling the gradient of strains with factor α (αFEM) (2009, background): “For the first drawback, many assumed strain or mixed models have been proposed in the past decades to reduce the stiffness of the standard FEM model [2,8,22,24,28,29,31,32,34,35,37,40,42].”