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

@inproceedings{Garoni2018DiscontinuousGD,
title={Discontinuous Galerkin Discretization of the Heat Equation in Any Dimension : the Spectral Symbol},
author={Carlo Garoni and Rolf Krause},
year={2018}
}

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