Sciweavers

SIAMNUM
2010

A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation

12 years 10 months ago
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation
We derive a posteriori error estimates for the discretization of the heat equation in a unified and fully discrete setting comprising the discontinuous Galerkin, finite volume, mixed finite element, and conforming and nonconforming finite element methods in space and the backward Euler scheme in time. Our estimates are based on a H1-conforming reconstruction of the potential, continuous and piecewise affine in time, and a locally conservative H(div)-conforming reconstruction of the flux, piecewise constant in time. They yield a guaranteed and fully computable upper bound on the error measured in the energy norm augmented by a dual norm of the time derivative. Localin-time lower bounds are also derived; for nonconforming methods on time-varying meshes, the lower bounds require a mild parabolic-type constraint on the meshsize. Key words. heat equation, unified framework, a posteriori estimate, discontinuous Galerkin, finite volumes, mixed finite elements, conforming finite elements, nonc...
Alexandre Ern, Martin Vohralík
Added 21 May 2011
Updated 21 May 2011
Type Journal
Year 2010
Where SIAMNUM
Authors Alexandre Ern, Martin Vohralík
Comments (0)