Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates
Numerical Analysis
2012-05-15 v1
Abstract
The multiadaptive continuous/discontinuous Galerkin methods mcG(q) and mdG(q) for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution. In this paper, we prove general order a priori error estimates for the mcG(q) and mdG(q) methods. To prove the error estimates, we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution. The estimates then follow from interpolation estimates, together with stability estimates for the discrete dual solution.
Cite
@article{arxiv.1205.2995,
title = {Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates},
author = {Anders Logg},
journal= {arXiv preprint arXiv:1205.2995},
year = {2012}
}