Polygonal finite elements for incompressible fluid flow

[1]  Clark R. Dohrmann,et al.  Stabilization of Low-order Mixed Finite Elements for the Stokes Equations , 2004, SIAM J. Numer. Anal..

[2]  C. S. Jog,et al.  Stability of finite element models for distributed-parameter optimization and topology design , 1996 .

[3]  P. Milbradt,et al.  Polytope finite elements , 2008 .

[4]  K. Bathe,et al.  The inf-sup test , 1993 .

[5]  R. A. Nicolaides,et al.  Stable and Semistable Low Order Finite Elements for Viscous Flows , 1985 .

[6]  G. Paulino,et al.  PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab , 2012 .

[7]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[8]  I. Babuska.  Error-bounds for finite element method , 1971 .

[9]  Glaucio H. Paulino,et al.  Honeycomb Wachspress finite elements for structural topology optimization , 2009 .

[10]  John E. Bolander,et al.  Automated Modeling of Three‐Dimensional Structural Components Using Irregular Lattices , 2005 .

[11]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[12]  F. Brezzi,et al.  Basic principles of Virtual Element Methods , 2013 .

[13]  P. Le Tallec,et al.  On the convergence of the bilinear-velocity constant-pressure finite element method in viscous flow , 1986 .

[14]  Pierre Alliez,et al.  Optimizing Voronoi Diagrams for Polygonal Finite Element Computations , 2010, IMR.

[15]  Mohamed S. Ebeida,et al.  Uniform Random Voronoi Meshes , 2011, IMR.

[16]  N. Sukumar,et al.  Archives of Computational Methods in Engineering Recent Advances in the Construction of Polygonal Finite Element Interpolants , 2022 .

[17]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[18]  Zhiqiang Cai,et al.  An error estimate for two-dimensional Stokes driven cavity flow , 2008, Math. Comput..

[19]  Annalisa Buffa,et al.  Mimetic finite differences for elliptic problems , 2009 .

[20]  E. T. Olsen,et al.  Obtaining error estimates for optimally constrained incompressible finite elements , 1984 .

[21]  J. Guermond,et al.  Theory and practice of finite elements , 2004 .

[22]  D. Malkus.  Eigenproblems associated with the discrete LBB condition for incompressible finite elements , 1981 .

[23]  J. P. Benque,et al.  A finite element method for Navier-Stokes equations , 1980 .

[24]  Chandrajit L. Bajaj,et al.  Quadratic serendipity finite elements on polygons using generalized barycentric coordinates , 2011, Math. Comput..

[25]  Vivette Girault,et al.  Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.

[26]  A. Huerta,et al.  Finite Element Methods for Flow Problems , 2003 .

[27]  Robert L. Lee,et al.  The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2 , 1981 .

[28]  E. Wachspress,et al.  A Rational Finite Element Basis , 1975 .

[29]  Gianmarco Manzini,et al.  Error Analysis for a Mimetic Discretization of the Steady Stokes Problem on Polyhedral Meshes , 2010, SIAM J. Numer. Anal..

[30]  R. A. Nicolaides,et al.  On the stability of bilinear-constant velocity-pressure finite elements , 1984 .

[31]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[32]  Pavel B. Bochev,et al.  A Taxonomy of Consistently Stabilized Finite Element Methods for the Stokes Problem , 2004, SIAM J. Sci. Comput..

[33]  David J. Silvester.  Optimal low order finite element methods for incompressible flow , 1994 .

[34]  Anupam Saxena,et al.  A Material-Mask Overlay Strategy for Continuum Topology Optimization of Compliant Mechanisms Using Honeycomb Discretization , 2008 .

[35]  Ellen Kuhl,et al.  Diamond elements: a finite element/discrete‐mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity , 2007, International Journal for Numerical Methods in Engineering.

[36]  Jirí Kosinka,et al.  On the injectivity of Wachspress and mean value mappings between convex polygons , 2010, Adv. Comput. Math..

[37]  M. Shashkov,et al.  A new discretization methodology for diffusion problems on generalized polyhedral meshes , 2007 .

[38]  Glaucio H. Paulino,et al.  Polygonal finite elements for topology optimization: A unifying paradigm , 2010 .

[39]  M. M. Rashid,et al.  A three‐dimensional finite element method with arbitrary polyhedral elements , 2006 .

[40]  Konstantin Lipnikov,et al.  A Mimetic Discretization of the Stokes Problem with Selected Edge Bubbles , 2010, SIAM J. Sci. Comput..

[41]  Somnath Ghosh,et al.  Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method , 2011 .

[42]  Roger Pierre,et al.  Simple C o approximations for the computation of incompressible flows , 1988 .

[43]  M. Fortin,et al.  Finite Elements for the Stokes Problem , 2008 .

[44]  N. Sukumar,et al.  Generalized Gaussian quadrature rules on arbitrary polygons , 2010 .

[45]  N. Sukumar,et al.  Conforming polygonal finite elements , 2004 .

[46]  M. Fortin,et al.  A stable finite element for the stokes equations , 1984 .

[47]  Stéphane Bordas,et al.  Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping , 2009 .

[48]  Chandrajit L. Bajaj,et al.  Error estimates for generalized barycentric interpolation , 2010, Adv. Comput. Math..

[49]  Gianmarco Manzini,et al.  Mimetic finite difference method for the Stokes problem on polygonal meshes , 2009, J. Comput. Phys..

[50]  Kai Hormann,et al.  Maximum Entropy Coordinates for Arbitrary Polytopes , 2008, Comput. Graph. Forum.

[51]  Glaucio H. Paulino,et al.  PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes , 2012 .

[52]  Gianmarco Manzini,et al.  Arbitrary-Order Nodal Mimetic Discretizations of Elliptic Problems on Polygonal Meshes , 2011, SIAM J. Numer. Anal..

[53]  Mark Meyer,et al.  Generalized Barycentric Coordinates on Irregular Polygons , 2002, J. Graphics, GPU, & Game Tools.

[54]  Pavel B. Bochev,et al.  On the Finite Element Solution of the Pure Neumann Problem , 2005, SIAM Rev..

[55]  O. Botella,et al.  BENCHMARK SPECTRAL RESULTS ON THE LID-DRIVEN CAVITY FLOW , 1998 .

[56]  Dominik Schötzau,et al.  hp -finite element simulations for Stokes flow—stable and stabilized , 1999 .

[57]  Kai Hormann,et al.  A general construction of barycentric coordinates over convex polygons , 2006, Adv. Comput. Math..

[58]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

[59]  A. Huerta,et al.  Finite Element Methods for Flow Problems , 2003 .

[60]  J. Bolander,et al.  Fracture analyses using spring networks with random geometry , 1998 .

[61]  J. Douglas,et al.  Stabilized mixed methods for the Stokes problem , 1988 .