On the Stability of the Discontinuous Galerkin Method for the Heat Equation

This paper analyzes stability properties of a class of discontinuous Galerkin methods for the heat equation. It is shown that the finite element projection associated with these methods is stable with respect to a mesh-dependent norm--a discrete analogue of the space-time L2-norm. Optimal order-regu...

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Veröffentlicht in:	SIAM journal on numerical analysis 1997-02, Vol.34 (1), p.389-401
Hauptverfasser:	Ch. G. Makridakis, Babuska, I.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied mathematics Approximation Computational techniques Degrees of polynomials Error analysis Estimates Estimation methods Exact sciences and technology Finite element method Finite-element and galerkin methods Galerkin methods Heat equation Mathematical discontinuity Mathematical methods in physics Mathematics Methods Norms Numerical analysis Numerical analysis. Scientific computation Numerical approximation and analysis Ordinary and partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Physics Polynomials Sciences and techniques of general use Spacetime
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Beschreibung
Zusammenfassung:	This paper analyzes stability properties of a class of discontinuous Galerkin methods for the heat equation. It is shown that the finite element projection associated with these methods is stable with respect to a mesh-dependent norm--a discrete analogue of the space-time L2-norm. Optimal order-regularity error bounds in L2([ 0, T ]; L2(Ω)) are derived.
ISSN:	0036-1429 1095-7170
DOI:	10.1137/S0036142994261658