dg1d_burgers

dg1d_burgers, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the time dependent 1D Burgers Equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.

A 1D version of the time dependent Burgers equation has the form

        PDE:
          du/dt + du^2/dx = 0  for -1 < x < +1
        IC:
          epsilon = 0.1
          u(x,0) = - tanh ( ( x + 0.5 ) / ( 2 * epsilon ) ) + 1.0

Licensing:

      Permission to use this software for noncommercial
      research and educational purposes is hereby granted
      without fee.  Redistribution, sale, or incorporation
      of this software into a commercial product is prohibited.

      THE AUTHORS OR PUBLISHER DISCLAIMS ANY AND ALL WARRANTIES
      WITH REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED
      WARRANTIES OF MERCHANTABILITY AND FITNESS FOR ANY
      PARTICULAR PURPOSE.  IN NO EVENT SHALL THE AUTHORS OR
      THE PUBLISHER BE LIABLE FOR ANY SPECIAL, INDIRECT OR
      CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
      RESULTING FROM LOSS OF USE, DATA OR PROFITS.

Languages:

dg1d_burgers is available in a MATLAB version.

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fem1d, a MATLAB code which applies the finite element method to a linear two point boundary value problem in a 1D region.

fem1d_bvp_linear, a MATLAB code which applies the finite element method, with piecewise linear elements, to a two point boundary value problem in one spatial dimension.

Author:

The original MATLAB source code was written by Jan Hesthaven and Tim Warburton.

Reference:

Jan Hesthaven, Tim Warburton,
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications,
Springer, 2007,
ISBN: 978-0387720654.

Source Code:

BuildMaps1D.m, sets up connectivity and boundary tables for the nodes.
Burgers1D.m, integrates the 1D Burgers equation over a time interval, given an initial condition.
BurgersRHS1D.m, evaluates the right hand side flux in the Burgers equation.
Connect1D.m, builds the global connectivity arrays.
Dmatrix1D.m, initializes the differentiation matrices.
GeometricFactors1D.m, computes metric elements for the local mappings.
Globals1D.m, declares global variables.
GradJacobiP.m, evaluates derivatives of the Jacobi polynomial.
GradVandermonde1D.m, initialializes the gradient of the modal basis.
JacobiGL.m, compute the Nth order Gauss-Lobatto quadrature points.
JacobiGQ.m, compute the Nth order Gauss quadrature points.
JacobiP.m, evaluate the Jacobi polynomial.
Lift1D.m, compute the surface integral term for the Discontinuous Galerkin formulation.
MeshGen1D.m, generate a uniform spatial grid.
Normals1D.m, compute the outward normals at element faces.
StartUp1D.m, sets building operators, grid, metric and connectivity.
Vandermonde1D.m, initialize the 1D Vandermonde matrix.

Last modified on 05 January 2019.