Error estimate of fully discrete discontinuous Galerkin approximation for the viscoelasticity type equation

In this paper we develop fully discrete discontinuous Galerkin approximation using symmetric interior penalty method. We construct finite element spaces which consist of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection of u and prove its optimal convergence. We...

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Veröffentlicht in:	Journal of applied mathematics & computing 2011-10, Vol.37 (1-2), p.473-495
Hauptverfasser:	Ohm, Mi Ray, Lee, Hyun Young, Shin, Jun Yong
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied mathematics Approximation Combinatorics Computational Mathematics and Numerical Analysis Convergence Estimates Fines & penalties Mathematical analysis Mathematical and Computational Engineering Mathematics Mathematics and Statistics Mathematics of Computing Methods Partial differential equations Studies Theory of Computation Viscoelasticity
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Zusammenfassung:	In this paper we develop fully discrete discontinuous Galerkin approximation using symmetric interior penalty method. We construct finite element spaces which consist of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection of u and prove its optimal convergence. We develop fully discrete discontinuous Galerkin approximations and prove the optimal convergence in ℓ ∞ ( L 2 ) normed space.
ISSN:	1598-5865 1865-2085
DOI:	10.1007/s12190-010-0445-0