Discontinuous Galerkin Discretization of the Heat Equation in Any Dimension : the Spectral Symbol

  title={Discontinuous Galerkin Discretization of the Heat Equation in Any Dimension : the Spectral Symbol},
  author={Carlo Garoni and Rolf Krause},
The multidimensional heat equation, along with its more general version involving variable diffusion coefficients, is discretized by a discontinuous Galerkin (DG) method in time and a finite element (FE) method of arbitrary regularity in space. We show that the resulting space-time discretization matrices enjoy an asymptotic spectral distribution as the mesh fineness increases, and we determine the associated spectral symbol, i.e., the function that carefully describes the spectral distribution… CONTINUE READING


Publications referenced by this paper.
Showing 1-10 of 31 references

A Practical Guide to Splines

  • C. De Boor
  • Revised ed., Springer, New York
  • 2001
Highly Influential
7 Excerpts

Matrix Analysis

  • R. Bhatia
  • Springer, New York
  • 1997
Highly Influential
9 Excerpts

Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain

  • P. Jamet
  • SIAM J. Numer. Anal., 15
  • 1978
Highly Influential
4 Excerpts

On a finite element method for solving the neutron transport equation

  • P. Lesaint, P. A. Raviart
  • Chapter 4 (pp. 89–123) of the book “Mathematical…
  • 1974
Highly Influential
4 Excerpts

Lusin theorem

  • C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, H. Speleers
  • GLT sequences and matrix computations: an…
  • 2017
2 Excerpts

Similar Papers

Loading similar papers…