Quasi-Wilson nonconforming element approximation for nonlinear dual phase lagging heat conduction equations

Abstract

Accuracy analysis of quasi-Wilson nonconforming element for nonlinear dual phase lagging heat conduction equations is discussed and higher order error estimates are derived under semi-discrete and fully-discrete schemes. Since the nonconforming part of quasi-Wilson element is orthogonal to biquadratic polynomials in a certain sense, it can be proved that the compatibility error of this element is of order O(h2)/O(h3) when the exact solution belongs to H3(Ω)/H4(Ω), which is one/two order higher than its interpolation error. Based on the above results, the superclose properties in L2-norm and broken H1-norm are deduced by using high accuracy analysis of bilinear finite element. Moreover, the global superconvergence in broken H1-norm is derived by interpolation postprocessing technique. And then, the extrapolation result with order O(h3) in broken H1-norm is obtained by constructing a new extrapolation scheme properly, which is two order higher than the usual error estimate. Finally, optimal order error estimates are deduced for a proposed fully-discrete approximate scheme.