The Mathematical Institute, University of Oxford, Eprints Archive

A Gagliardo-Nirenberg inequality, with application to duality-based a posteriori error estimation in the L1 norm

Suli, Endre (2006) A Gagliardo-Nirenberg inequality, with application to duality-based a posteriori error estimation in the L1 norm. Technical Report. Unspecified. (Submitted)

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Abstract

We establish the Gagliardo-Nirenberg-type multiplicative interpolation inequality $ \[ \|v\|_{{\rm L}1(\mathbb{R}^n)} \leq C \|v\|^{1/2}_{{\rm Lip}'(\mathbb{R}^n)} \|v\|^{1/2}_{{\rm BV}(\mathbb{R}^n)}\qquad \forall v \in {\rm BV}(\mathbb{R}^n), \] $ where $C$ is a positive constant, independent of $v$. We then use a local version of this inequality to derive an a posteriori error bound in the ${\rm L}1(\Omega')$ norm, with $\bar\Omega' \subset\Omega=(0,1)^n$, for a finite-element approximation to a boundary value problem for a first-order linear hyperbolic equation, under the limited regularity requirement that the solution to the problem belongs to ${\rm BV}(\Omega)$.

Dedicated to Professor Boško S Jovanovic on the occasion of his sixtieth birthday

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1105
Deposited By:Lotti Ekert
Deposited On:11 May 2011 10:59
Last Modified:11 May 2011 10:59

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