An efficient nodal integration with quadratic exactness for three-dimensional meshfree Galerkin methods

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2016.06.003 ◽

2016 ◽

Vol 70 ◽

pp. 99-113 ◽

Author(s):

Bingbing Wang ◽

Qinglin Duan ◽

Yulong Shao ◽

Xikui Li ◽

Dixiong Yang ◽

...

Keyword(s):

Three Dimensional ◽

Galerkin Methods ◽

Nodal Integration

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Stabilized hp-DGFEM for Incompressible Flow

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202503002970 ◽

2003 ◽

Vol 13 (10) ◽

pp. 1413-1436 ◽

Author(s):

D. Schötzau ◽

C. Schwab ◽

A. Toselli

Keyword(s):

Boundary Layer ◽

Discontinuous Galerkin ◽

Incompressible Flow ◽

Discontinuous Galerkin Methods ◽

Stokes Problem ◽

Three Dimensional ◽

Stability Result ◽

Approximation Order ◽

Galerkin Methods ◽

We consider stabilized mixed hp-discontinuous Galerkin methods for the discretization of the Stokes problem in three-dimensional polyhedral domains. The methods are stabilized with a term penalizing the pressure jumps. For this approach it is shown that ℚk-ℚk and ℚk-ℚk-1 elements satisfy a generalized inf–sup condition on geometric edge and boundary layer meshes that are refined anisotropically and non quasi-uniformly towards faces, edges, and corners. The discrete inf–sup constant is proven to be independent of the aspect ratios of the anisotropic elements and to decrease as k-1/2 with the approximation order. We also show that the generalized inf–sup condition leads to a global stability result in a suitable energy norm.

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Three dimensional discontinuous Galerkin methods for Euler equations on adaptive conforming meshes

Computer Physics Communications ◽

10.1016/j.cpc.2011.01.001 ◽

2011 ◽

Vol 182 (9) ◽

pp. 1771-1775 ◽

Author(s):

Xijun Yu ◽

Di Wu ◽

Yun Xu

Keyword(s):

Euler Equations ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Three Dimensional ◽

Galerkin Methods ◽

Conforming Meshes

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Interpolatory super-convergent discontinuous Galerkin methods for nonlinear reaction diffusion equations on three dimensional domains

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2020.105388 ◽

2020 ◽

Vol 90 ◽

pp. 105388

Author(s):

Paul Castillo ◽

Sergio Gómez

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Three Dimensional ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Galerkin Methods ◽

Nonlinear Reaction

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Discontinuous Galerkin Methods Using an hp-Multigrid Solver for Inviscid Compressible Flows on Three-dimensional Unstructured Meshes

44th AIAA Aerospace Sciences Meeting and Exhibit ◽

10.2514/6.2006-107 ◽

2006 ◽

Author(s):

Cristian Nastase ◽

Dimitri Mavriplis

Keyword(s):

Discontinuous Galerkin ◽

Compressible Flows ◽

Discontinuous Galerkin Methods ◽

Three Dimensional ◽

Unstructured Meshes ◽

Galerkin Methods ◽

Multigrid Solver ◽

Inviscid Compressible Flows

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Quadratically consistent nodal integration for second order meshfree Galerkin methods

Computational Mechanics ◽

10.1007/s00466-014-0989-1 ◽

2014 ◽

Vol 54 (2) ◽

pp. 353-368 ◽

Author(s):

Qinglin Duan ◽

Bingbing Wang ◽

Xin Gao ◽

Xikui Li

Keyword(s):

Second Order ◽

Galerkin Methods ◽

Nodal Integration

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Solving the Three-Dimensional Time-Harmonic Maxwell Equations by Discontinuous Galerkin Methods Coupled to an Integral Representation

Applied Condition Monitoring - Multiphysics Modelling and Simulation for Systems Design and Monitoring ◽

10.1007/978-3-319-14532-7_41 ◽

2015 ◽

pp. 401-408

Author(s):

Nabil Gmati ◽

Stéphane Lanteri ◽

Anis Mohamed

Keyword(s):

Integral Representation ◽

Discontinuous Galerkin ◽

Maxwell Equations ◽

Discontinuous Galerkin Methods ◽

Three Dimensional ◽

Galerkin Methods ◽

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A nodal integration scheme for meshfree Galerkin methods using the virtual element decomposition

International Journal for Numerical Methods in Engineering ◽

10.1002/nme.6304 ◽

2020 ◽

Vol 121 (10) ◽

pp. 2174-2205 ◽

Author(s):

R. Silva‐Valenzuela ◽

A. Ortiz‐Bernardin ◽

N. Sukumar ◽

E. Artioli ◽

N. Hitschfeld‐Kahler

Keyword(s):

Integration Scheme ◽

Galerkin Methods ◽

Nodal Integration ◽

Virtual Element

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Perfectly Matched Layer Formalism for Non-Convex Domains for the Time Maxwell Equations: Application to Finite Volumes, Finite Differences and Three-Dimensional Discontinuous Galerkin Methods

Proceedings of the Seventh International Conference on Engineering Computational Technology ◽

10.4203/ccp.94.85 ◽

2010 ◽

Author(s):

J.B. Laurent ◽

P.A. Mazet ◽

X. Ferrieres

Keyword(s):

Discontinuous Galerkin ◽

Finite Differences ◽

Maxwell Equations ◽

Discontinuous Galerkin Methods ◽

Three Dimensional ◽

Perfectly Matched Layer ◽

Finite Volumes ◽

Galerkin Methods ◽

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A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods

Journal of Computational Physics ◽

10.1016/j.jcp.2007.10.004 ◽

2008 ◽

Vol 227 (3) ◽

pp. 2044-2072 ◽

Author(s):

Victorita Dolean ◽

Stéphane Lanteri ◽

Ronan Perrussel

Keyword(s):

Domain Decomposition ◽

Discontinuous Galerkin ◽

Decomposition Method ◽

Maxwell Equations ◽

Discontinuous Galerkin Methods ◽

Domain Decomposition Method ◽

Three Dimensional ◽

Galerkin Methods ◽

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A three-dimensional nodal-based implementation of a family of discontinuous Galerkin methods for elasticity problems

Computers & Structures ◽

10.1016/j.compstruc.2008.11.009 ◽

2009 ◽

Vol 87 (3-4) ◽

pp. 141-150 ◽

Author(s):

R. Liu ◽

M.F. Wheeler ◽

C.N. Dawson

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Three Dimensional ◽

Galerkin Methods ◽

Elasticity Problems

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