Interpolation Error-Based A Posteriori Error Estimation for Parabolic and Elliptic Equations
A new a posteriori error estimation strategy based on the Lobatto interpolant will be presented. This approach offers several advantages over other methods: i) it is easy to compute; ii) it is asymptotically exact; iii) it provides asymptotically exact estimates one order higher than the current order; iv) it provides error indicators on elements with irregular nodes. I will develop the estimates for linear two-point boundary value problems and one- dimensional parabolic equations. I will discuss extensions of the method to three dimensions and the impact of different bases on the error estimates.