DGIRM: Discontinuous Galerkin based isogeometric residual minimization for the Stokes problem

[1]  Rob Stevenson,et al.  A robust Petrov-Galerkin discretisation of convection-diffusion equations , 2014, Comput. Math. Appl..

[2]  R. Bank,et al.  A class of iterative methods for solving saddle point problems , 1989 .

[3]  Kenneth E. Jansen,et al.  A better consistency for low-order stabilized finite element methods , 1999 .

[4]  Giancarlo Sangalli,et al.  IsoGeometric Analysis: Stable elements for the 2D Stokes equation , 2011 .

[5]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[6]  Lisandro Dalcin,et al.  PetIGA: High-Performance Isogeometric Analysis , 2013, ArXiv.

[7]  Norbert Heuer,et al.  Robust DPG Method for Convection-Dominated Diffusion Problems , 2013, SIAM J. Numer. Anal..

[8]  T. Hughes,et al.  Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations , 2010 .

[9]  Thomas J. R. Hughes,et al.  Isogeometric Analysis for Topology Optimization with a Phase Field Model , 2012 .

[10]  Lisandro Dalcin,et al.  Energy exchange analysis in droplet dynamics via the Navier–Stokes–Cahn–Hilliard model , 2015, Journal of Fluid Mechanics.

[11]  T. Hughes,et al.  Isogeometric Fluid–structure Interaction Analysis with Applications to Arterial Blood Flow , 2006 .

[12]  T. Hughes,et al.  Isogeometric analysis of the Cahn–Hilliard phase-field model , 2008 .

[13]  T. Hughes,et al.  Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement , 2005 .

[14]  Victor M. Calo,et al.  Isogeometric Variational Multiscale Large-Eddy Simulation of Fully-developed Turbulent Flow over a Wavy Wall , 2012 .

[15]  Patrick Amestoy,et al.  A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling , 2001, SIAM J. Matrix Anal. Appl..

[16]  Yong Liu,et al.  Stabilized finite element method for viscoplastic flow: formulation and a simple progressive solution strategy , 2001 .

[17]  Victor M. Calo,et al.  Mathematical modeling of coupled drug and drug-encapsulated nanoparticle transport in patient-specific coronary artery walls , 2012 .

[18]  Jesse Chan,et al.  A Minimum-Residual Finite Element Method for the Convection-Diffusion Equation , 2013 .

[19]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[20]  Jesse Chan,et al.  Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems , 2014, Comput. Math. Appl..

[21]  Victor M. Calo,et al.  A Stable Discontinuous Galerkin Based Isogeometric Residual Minimization for the Stokes Problem , 2020, ICCS.

[22]  Norbert Heuer,et al.  A robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms , 2014, Comput. Math. Appl..

[23]  Victor M. Calo,et al.  Fast isogeometric solvers for explicit dynamics , 2014 .

[24]  Gao Liping,et al.  Stability and Super Convergence Analysis of ADI-FDTD for the 2D Maxwell Equations in a Lossy Medium , 2012 .

[25]  L. Franca,et al.  Stabilized finite element methods. II: The incompressible Navier-Stokes equations , 1992 .

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

[27]  Victor M. Calo,et al.  PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces , 2016, J. Comput. Sci..

[28]  Leszek Demkowicz,et al.  An Overview of the Discontinuous Petrov Galerkin Method , 2014 .

[29]  Marcin Los,et al.  Isogeometric residual minimization (iGRM) for non-stationary Stokes and Navier-Stokes problems , 2021, Comput. Math. Appl..

[30]  Victor M. Calo,et al.  An energy-stable convex splitting for the phase-field crystal equation , 2014, 1405.3488.

[31]  T. Hughes,et al.  Stabilized finite element methods. I: Application to the advective-diffusive model , 1992 .

[32]  Marcin Los,et al.  Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection-diffusion problems , 2020, Comput. Math. Appl..

[33]  Victor M. Calo,et al.  A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high‐order B‐spline finite elements , 2012 .

[34]  Elizabeth R. Jessup,et al.  A Technique for Accelerating the Convergence of Restarted GMRES , 2005, SIAM J. Matrix Anal. Appl..

[35]  F. Brezzi,et al.  A relationship between stabilized finite element methods and the Galerkin method with bubble functions , 1992 .

[36]  Thomas J. R. Hughes,et al.  The Stokes problem with various well-posed boundary conditions - Symmetric formulations that converge for all velocity/pressure spaces , 1987 .

[37]  Ewa Grabska,et al.  Graph Transformations for Modeling hp-Adaptive Finite Element Method with Mixed Triangular and Rectangular Elements , 2009, ICCS.

[38]  Victor M. Calo,et al.  Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers , 2014, Comput. Math. Appl..

[39]  Marlis Hochbruck,et al.  Convergence of an ADI splitting for Maxwell’s equations , 2015, Numerische Mathematik.

[40]  Patrick Amestoy,et al.  Hybrid scheduling for the parallel solution of linear systems , 2006, Parallel Comput..

[41]  Leszek Demkowicz,et al.  Verification of goal-oriented HP-adaptivity , 2005 .

[42]  Thomas J. R. Hughes,et al.  Stabilized Methods for Compressible Flows , 2010, J. Sci. Comput..

[43]  Krzysztof Boryczko,et al.  A Parallel Preconditioning for the Nonlinear Stokes Problem , 2005, PPAM.

[44]  Wolfgang Dahmen,et al.  On the stability of DPG formulations of transport equations , 2015, Math. Comput..

[45]  Yuri Bazilevs,et al.  High-performance computing of wind turbine aerodynamics using isogeometric analysis , 2011 .

[46]  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 .

[47]  Maciej Paszyński,et al.  Fully automatic hp adaptive finite element method for the Stokes problem in two dimensions , 2008 .

[48]  Guido Kanschat,et al.  Local Discontinuous Galerkin Methods for the Stokes System , 2002, SIAM J. Numer. Anal..