A posteriori error estimates for fully discrete fractional-step ϑ-approximations for the heat equation

2014/04/02 by Fotini Karakatsani, Fotini, Karakatsani
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Numerical methods in inverse problems #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1404.0497

Abstract

We derive optimal order a posteriori error estimates for fully discrete approximations of the initial-boundary value problem for the heat equation. For the discretization in time we apply the fractional-step ϑ-scheme and for the discretization in space the finite element method with finite element spaces that are allowed to change with time. The first optimal order a posteriori error estimates in L^∞(0, T ; L²(\varOmega)) are derived by applying the reconstruction technique.

Related

• Optimal L^∞(L²) and L¹(L²) a posteriori error estimates for the fully discrete approximations of time fractional parabolic differential equations
• On the efficiency of a posteriori error estimators for parabolic partial differential equations in the energy norm
• Long time L^\∞(L²) a posteriori error estimates for fully\n discrete parabolic problems
• Conditional a posteriori error bounds for high order DG time stepping approximations of semilinear heat models with blow-up
• Error Analysis of Finite Element Methods for Space-Fractional Parabolic Equations