Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations

Journal of Computational Physics ◽

10.1016/j.jcp.2019.03.021 ◽

2019 ◽

Vol 388 ◽

pp. 90-102 ◽

Author(s):

Yuan Liu ◽

Yingda Cheng ◽

Shanqin Chen ◽

Yong-Tao Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Reaction Diffusion ◽

Sparse Grids ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

High Dimensional ◽

Galerkin Methods ◽

Implicit Integration

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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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Krylov implicit integration factor methods for spatial discretization on high dimensional unstructured meshes: Application to discontinuous Galerkin methods

Journal of Computational Physics ◽

10.1016/j.jcp.2011.01.010 ◽

2011 ◽

Vol 230 (11) ◽

pp. 4336-4352 ◽

Author(s):

Shanqin Chen ◽

Yong-Tao Zhang

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Unstructured Meshes ◽

High Dimensional ◽

Galerkin Methods ◽

Spatial Discretization ◽

Implicit Integration ◽

Implicit Integration Factor Methods

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Analysis of direct discontinuous Galerkin methods for multi-dimensional convection–diffusion equations

Numerische Mathematik ◽

10.1007/s00211-021-01183-x ◽

2021 ◽

Vol 147 (4) ◽

pp. 839-867

Author(s):

Hailiang Liu

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion

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A Family of Characteristic Discontinuous Galerkin Methods for Transient Advection-Diffusion Equations and Their Optimal-Order L^2 Error Estimates

Communications in Computational Physics ◽

10.4208/cicp.2009.v6.p203 ◽

2009 ◽

pp. 203-230 ◽

Author(s):

Kaixin Wang ◽

Hong Wang ◽

Mohamed Al-Lawatia ◽

Hongxing Rui

Keyword(s):

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Optimal Order ◽

Galerkin Methods ◽

Advection Diffusion

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Fast implicit integration factor method for nonlinear space Riesz fractional reaction–diffusion equations

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112935 ◽

2020 ◽

Vol 378 ◽

pp. 112935 ◽

Author(s):

Huan-Yan Jian ◽

Ting-Zhu Huang ◽

Xian-Ming Gu ◽

Xi-Le Zhao ◽

Yong-Liang Zhao

Keyword(s):

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Diffusion Equations ◽

Implicit Integration ◽

Factor Method ◽

Fractional Reaction

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Stability analysis and error estimates of local discontinuous Galerkin methods for convection–diffusion equations on overlapping meshes

BIT Numerical Mathematics ◽

10.1007/s10543-019-00757-4 ◽

2019 ◽

Vol 59 (4) ◽

pp. 853-876 ◽

Author(s):

Jie Du ◽

Yang Yang ◽

Eric Chung

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Spacetime discontinuous Galerkin methods for convection-diffusion equations

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-016-0169-3 ◽

2016 ◽

Vol 47 (2) ◽

pp. 561-573 ◽

Author(s):

Sandra May

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion

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Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

Computational Optimization and Applications ◽

10.1007/s10589-014-9691-7 ◽

2014 ◽

Vol 62 (1) ◽

pp. 291-321 ◽

Author(s):

Hamdullah Yücel ◽

Peter Benner

Keyword(s):

Optimal Control ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Optimal Control Problems ◽

Diffusion Equations ◽

Control Problems ◽

Galerkin Methods ◽

Constrained Optimal Control ◽

Convection Diffusion

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Local Discontinuous Galerkin methods for fractional diffusion equations

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2013091 ◽

2013 ◽

Vol 47 (6) ◽

pp. 1845-1864 ◽

Author(s):

W.H. Deng ◽

J.S. Hesthaven

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Galerkin Methods ◽

Fractional Diffusion Equations ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods

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Discontinuous Galerkin Methods and Their Adaptivity for the Tempered Fractional (Convection) Diffusion Equations

Journal of Computational Mathematics ◽

10.4208/jcm.1906-m2019-0040 ◽

2020 ◽

Vol 38 (6) ◽

pp. 809-837

Author(s):

Xudong Wang & Weihua Deng

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Diffusion Equations ◽

Galerkin Methods ◽

Convection Diffusion

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