Computer Methods in Applied Mechanics and Engineering
A discourse on the stability conditions for mixed finite element formulations
Computer Methods in Applied Mechanics and Engineering
Mixed finite element methods—reduced and selective integration techniques: a unification of concepts
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Volume conserving finite element simulations of deformable models
ACM SIGGRAPH 2007 papers
A regularized Lagrangian finite point method for the simulation of incompressible viscous flows
Journal of Computational Physics
Divergence-Free Kernel Methods for Approximating the Stokes Problem
SIAM Journal on Numerical Analysis
Finite deformation elasto-plastic modelling using an adaptive meshless method
Computers and Structures
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods
Computational Mechanics
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A novel maximum-entropy meshfree method that we recently introduced in Ortiz et al. (2010) [1] is extended to Stokes flow in two dimensions and to three-dimensional incompressible linear elasticity. The numerical procedure is aimed to remedy two outstanding issues in meshfree methods: the development of an optimal and stable formulation for incompressible media, and an accurate cell-based numerical integration scheme to compute the weak form integrals. On using the incompressibility constraint of the standard u-p formulation, a u-based formulation is devised by nodally averaging the hydrostatic pressure around the nodes. A modified Gauss quadrature scheme is employed, which results in a correction to the stiffness matrix that alleviates integration errors in meshfree methods, and satisfies the patch test to machine accuracy. The robustness and versatility of the maximum-entropy meshfree method is demonstrated in three-dimensional computations using tetrahedral background meshes for integration. The meshfree formulation delivers optimal rates of convergence in the energy and L^2-norms. Inf-sup tests are presented to demonstrate the stability of the maximum-entropy meshfree formulation for incompressible media problems.