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arXiv · 1205.2995

Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates

Anders Logg
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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.

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Anders Logg. 2012-05-14. Multiadaptive Galerkin Methods for ODEs III: A Priori Error Estimates. https://doi.org/10.1137/040604133

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