Abstract
EQ rot1 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 rot1 element. Finally, optimal error estimate is gained for a proposed fully-discrete scheme by different approaches from the previous literature.
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Supported by the National Natural Science Foundation of China (Nos. 10971203; 11101381), Tianyuan Mathematics 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).
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Zhao, Ym., Wang, Fl. & Shi, Dy. EQ rot1 nonconforming finite element method for nonlinear dual phase lagging heat conduction equations. Acta Math. Appl. Sin. Engl. Ser. 29, 201–214 (2013). https://doi.org/10.1007/s10255-013-0205-7
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DOI: https://doi.org/10.1007/s10255-013-0205-7
Keywords
- nonlinear dual phase lagging heat conduction equations
- EQ rot1 nonconforming finite element
- superclose and superconvergence
- extrapolation
- semi-discrete and fully-discrete schemes