dg1d_heat

dg1d_heat, a MATLAB code which uses the Discontinuous Galerkin Method (DG) to approximate a solution of the unsteady 1D heat Equation. The original version of the code was written by Jan Hesthaven and Tim Warburton.

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

        du/dt = d2u/dx2  for 0 < x < 2*pi
 
        u(0,t) = 0       Boundary conditions
        u(2*pi,t) = 0

        u(x,0) = sin(x)    Initial condition
      

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_heat is available in a MATLAB version.

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dg1d_heat_test

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Author:

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

Reference:

1. 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.
• 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.
• Heat1D.m, integrates the 1D heat equation over a time interval, given an initial condition.
• HeatCRHS1D.m, uses central flux to evaluate the right hand side flux in the heat equation.
• HeatCstabRHS1D.m, uses stabilized central flux to evaluate the right hand side flux in the heat equation.
• HeatLDGRHS1D.m, uses an LDG flux to evaluate the right hand side flux in the heat equation.
• 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.