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

EQ ₁ ^rot 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(h ²) one order higher than its interpolation error O(h), the superclose results of order O(h ²) in broken H ¹-norm are obtained. At the same time, the global superconvergence in broken H ¹-norm is deduced by interpolation postprocessing technique. Moreover, the extrapolation result with order O(h ⁴) is derived by constructing a new interpolation postprocessing operator and extrapolation scheme based on the known asymptotic expansion formulas of EQ ₁ ^rot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.