Stability Analysis of Discontinuous Galerkin Discrete Shock Profiles for Steady Scalar Conservation Laws

SIAM Journal on Numerical Analysis ◽

10.1137/15m1026808 ◽

2016 ◽

Vol 54 (1) ◽

pp. 187-209

Author(s):

Florent Renac

Keyword(s):

Stability Analysis ◽

Conservation Laws ◽

Discontinuous Galerkin ◽

Scalar Conservation Laws ◽

Shock Profiles ◽

Scalar Conservation

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Stationary Discrete Shock Profiles for Scalar Conservation Laws with a Discontinuous Galerkin Method

SIAM Journal on Numerical Analysis ◽

10.1137/14097906x ◽

2015 ◽

Vol 53 (4) ◽

pp. 1690-1715 ◽

Author(s):

Florent Renac

Keyword(s):

Conservation Laws ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Scalar Conservation Laws ◽

Shock Profiles ◽

Scalar Conservation

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Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics

Computers & Fluids ◽

10.1016/j.compfluid.2010.07.018 ◽

2011 ◽

Vol 46 (1) ◽

pp. 498-504 ◽

Author(s):

François Vilar ◽

Pierre-Henri Maire ◽

Rémi Abgrall

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Unstructured Grids ◽

Two Dimensional ◽

Scalar Conservation Laws ◽

One Dimensional ◽

Lagrangian Hydrodynamics ◽

Scalar Conservation

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A spacetime discontinuous Galerkin method for scalar conservation laws

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2004.01.028 ◽

2004 ◽

Vol 193 (33-35) ◽

pp. 3607-3631 ◽

Author(s):

Jayandran Palaniappan ◽

Robert B. Haber ◽

Robert L. Jerrard

Keyword(s):

Conservation Laws ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Scalar Conservation Laws ◽

Scalar Conservation

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The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1991250303371 ◽

1991 ◽

Vol 25 (3) ◽

pp. 337-361 ◽

Author(s):

Bernardo Cockburn ◽

Chi-Wang Shu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Conservation Laws ◽

Discontinuous Galerkin ◽

Galerkin Finite Element Method ◽

Scalar Conservation Laws ◽

Galerkin Finite Element ◽

Local Projection ◽

Discontinuous Galerkin Finite Element ◽

Scalar Conservation

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The local projection $P^0-P^1$-discontinuous-Galerkin finite element method for scalar conservation laws

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1989230405651 ◽

1989 ◽

Vol 23 (4) ◽

pp. 565-592 ◽

Author(s):

Guy Chavent ◽

Bernardo Cockburn

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Conservation Laws ◽

Discontinuous Galerkin ◽

Galerkin Finite Element Method ◽

Scalar Conservation Laws ◽

Galerkin Finite Element ◽

Local Projection ◽

Discontinuous Galerkin Finite Element ◽

Scalar Conservation

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Error estimates to smooth solutions of semi-discrete discontinuous Galerkin methods with quadrature rules for scalar conservation laws

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22089 ◽

2016 ◽

Vol 33 (2) ◽

pp. 467-488 ◽

Author(s):

Juntao Huang ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Quadrature Rules ◽

Galerkin Methods ◽

Smooth Solutions ◽

Scalar Conservation Laws ◽

Scalar Conservation

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Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws

SIAM Journal on Numerical Analysis ◽

10.1137/s0036142902404182 ◽

2004 ◽

Vol 42 (2) ◽

pp. 641-666 ◽

Author(s):

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Conservation Laws ◽

Error Estimates ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Methods ◽

Galerkin Methods ◽

Smooth Solutions ◽

Scalar Conservation Laws ◽

Runge Kutta ◽

Scalar Conservation

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Recovery-Based Error Estimator for the Discontinuous Galerkin Method for Nonlinear Scalar Conservation Laws in One Space Dimension

Journal of Scientific Computing ◽

10.1007/s10915-015-0030-7 ◽

2015 ◽

Vol 66 (2) ◽

pp. 459-476 ◽

Author(s):

Mahboub Baccouch

Keyword(s):

Conservation Laws ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

Space Dimension ◽

Error Estimator ◽

Scalar Conservation Laws ◽

Scalar Conservation ◽

Nonlinear Scalar Conservation Laws ◽

One Space Dimension

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Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws

SIAM Journal on Numerical Analysis ◽

10.1137/090771363 ◽

2010 ◽

Vol 48 (3) ◽

pp. 1038-1063 ◽

Author(s):

Qiang Zhang ◽

Chi-Wang Shu

Keyword(s):

Stability Analysis ◽

Galerkin Method ◽

Discontinuous Galerkin ◽

Discontinuous Galerkin Method ◽

A Priori ◽

Scalar Conservation Laws ◽

Third Order ◽

The Third ◽

Priori Error Estimates ◽

Scalar Conservation

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On the Convergence of Space-Time Discontinuous Galerkin Schemes for Scalar Conservation Laws

SIAM Journal on Numerical Analysis ◽

10.1137/15m102438x ◽

2016 ◽

Vol 54 (4) ◽

pp. 2452-2465 ◽

Author(s):

Georg May ◽

Mohammad Zakerzadeh

Keyword(s):

Conservation Laws ◽

Discontinuous Galerkin ◽

Scalar Conservation Laws ◽

Scalar Conservation

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