Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates

Science China Mathematics ◽

10.1007/s11425-013-4739-1 ◽

2013 ◽

Vol 56 (12) ◽

pp. 2645-2676 ◽

Author(s):

JianFang Lu ◽

Chi-Wang Shu ◽

MengPing Zhang

Keyword(s):

Random Walk ◽

Stability Analysis ◽

Error Estimate ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

A Priori ◽

Galerkin Methods ◽

Correlated Random Walk ◽

Density Dependent ◽

A Priori Error Estimate

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An a priori error estimate for the local discontinuous Galerkin method applied to two-dimensional shallow water and morphodynamic flow

Numerical Methods for Partial Differential Equations ◽

10.1002/num.21914 ◽

2014 ◽

Vol 31 (2) ◽

pp. 397-421 ◽

Author(s):

Chris Mirabito ◽

Clint Dawson ◽

Vadym Aizinger

Keyword(s):

Error Estimate ◽

Galerkin Method ◽

Shallow Water ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Priori ◽

Local Discontinuous Galerkin Method ◽

Two Dimensional ◽

A Priori Error Estimate ◽

Local Discontinuous Galerkin

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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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An optimal-order L2-error estimate for nonsymmetric discontinuous Galerkin methods for a parabolic equation in multiple space dimensions

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2009.02.006 ◽

2009 ◽

Vol 198 (27-29) ◽

pp. 2190-2197 ◽

Author(s):

Kaixin Wang ◽

Hong Wang ◽

Shuyu Sun ◽

Mary F. Wheeler

Keyword(s):

Parabolic Equation ◽

Error Estimate ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Optimal Order ◽

Galerkin Methods ◽

L2 Error Estimate

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Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for the time-dependent fourth order PDEs

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/2017017 ◽

2017 ◽

Vol 51 (5) ◽

pp. 1931-1955 ◽

Author(s):

Haijin Wang ◽

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Stability Analysis ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Fourth Order ◽

Discontinuous Galerkin Methods ◽

Time Dependent ◽

Galerkin Methods ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

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Discontinuous Galerkin methods on hp-anisotropic meshes I: a priori error analysis

International Journal of Computing Science and Mathematics ◽

10.1504/ijcsm.2007.016533 ◽

2007 ◽

Vol 1 (2/3/4) ◽

pp. 221 ◽

Author(s):

Emmanuil H. Georgoulis ◽

Edward Hall ◽

Paul Houston

Keyword(s):

Error Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

A Priori ◽

Galerkin Methods ◽

Anisotropic Meshes ◽

A Priori Error Analysis

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Stability analysis and error estimates of local discontinuous Galerkin methods with implicit–explicit time-marching for nonlinear convection–diffusion problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.02.067 ◽

2016 ◽

Vol 272 ◽

pp. 237-258 ◽

Author(s):

Haijin Wang ◽

Chi-Wang Shu ◽

Qiang Zhang

Keyword(s):

Stability Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Local Discontinuous Galerkin ◽

Local Discontinuous Galerkin Methods ◽

Time Marching ◽

Diffusion Problems

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An a priori error estimate for a temporally discontinuous Galerkin space–time finite element method for linear elasto- and visco-dynamics

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2019.03.025 ◽

2019 ◽

Vol 351 ◽

pp. 1-19

Author(s):

Simon Shaw

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Error Estimate ◽

Discontinuous Galerkin ◽

A Priori ◽

A Priori Error Estimate ◽

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The L$^2$-norm Stability Analysis of Runge--Kutta Discontinuous Galerkin Methods for Linear Hyperbolic Equations

SIAM Journal on Numerical Analysis ◽

10.1137/18m1230700 ◽

2019 ◽

Vol 57 (4) ◽

pp. 1574-1601 ◽

Author(s):

Yuan Xu ◽

Qiang Zhang ◽

Chi-wang Shu ◽

Haijin Wang

Keyword(s):

Stability Analysis ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Hyperbolic Equations ◽

Galerkin Methods ◽

Runge Kutta ◽

Linear Hyperbolic Equations

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A Priori and a Posteriori Error Analysis of the Discontinuous Galerkin Methods for Reissner-Mindlin Plates

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.11-m1111 ◽

2011 ◽

Vol 3 (6) ◽

pp. 649-662 ◽

Author(s):

Jun Hu ◽

Yunqing Huang

Keyword(s):

Discontinuous Galerkin ◽

Error Control ◽

Discontinuous Galerkin Methods ◽

A Priori ◽

Posteriori Error ◽

Mindlin Plate ◽

Galerkin Methods ◽

A Posteriori ◽

A Posteriori Error ◽

Posteriori Error Analysis

AbstractIn this paper, we apply an a posteriori error control theory that we develop in a very recent paper to three families of the discontinuous Galerkin methods for the Reissner-Mindlin plate problem. We derive robust a posteriori error estimators for them and prove their reliability and efficiency.

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Penalty-free discontinuous Galerkin methods for incompressible Navier–Stokes equations

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202513500826 ◽

2014 ◽

Vol 24 (06) ◽

pp. 1217-1236 ◽

Author(s):

Beatrice Riviere ◽

Shirin Sardar

Keyword(s):

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Stokes Equations ◽

A Priori ◽

Navier Stokes ◽

Galerkin Methods ◽

Navier Stokes Equations ◽

First Order ◽

Priori Error Estimates ◽

A first-order discontinuous Galerkin method is proposed for solving the steady-state incompressible Navier–Stokes equations. The stability of this penalty-free method is obtained by locally enriching the discrete space with a quadratic polynomial. A priori error estimates are derived. Numerical examples confirm the theoretical convergence.

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