EQ 1 rot nonconforming finite element method for nonlinear dual phase lagging heat conduction equations

Abstract

EQ1rot nonconforming finite element approximation to a class of nonlinear dual phase lagging heat conduction equations is discussed for semi-discrete and fully-discrete schemes. By use of a special property, that is, the consistency error of this element is of order O(h2) one order higher than its interpolation error O(h), the superclose results of order O(h2) in broken H1-norm are obtained. At the same time, the global superconvergence in broken H1-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h4) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ1rot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.