摘要
EQrot 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 Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-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 EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.
EQrot 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 Hi-norm are obtained. At the same time, the global superconvergence in broken Hi-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 EQrot element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.
基金
Supported by the National Natural Science Foundation of China (Nos. 10971203
11101381)
Tianyuan Mathe-matics Foundation of National Natural Science Foundation of China (No. 11026154)
Natural Science Foundation of Henan Province (No. 112300410026)
Natural Science Foundation of the Education Department of Henan Province (Nos. 2011A110020
12A110021)