JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 133-142.doi: 10.6040/j.issn.1671-9352.0.2024.006

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Superconvergence analysis of nonlinear Sobolev-Galpern equations

LI Suli, XIE Huazhao*   

  1. School of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450046, Henan, China
  • Published:2026-04-08

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Abstract: The nonlinear Sobolev-Galpern equations are studied with low order mixed finite element (Q11+Q01×Q10). By utilizing the high precision results of the finite element Q11+Q01×Q10, and mean-value technique, the superconvergence results of order O(h2)are obtained for the semi-discrete scheme of the equations. For the linearized fully discrete scheme, the superconvergence results of order O(h2+τ2)are also derived, here h is the subdivision parameter, τ is the time step. Finally, a numerical example is provided to confirm our theoretical analysis.

Key words: nonlinear Sobolev-Galpern equations, mixed finite element, linearized scheme, superconvergence analysis

CLC Number: 

  • O242.21
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