JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (2): 1-9.doi: 10.6040/j.issn.1671-9352.0.2024.109

   

Adaptive finite element method for two-dimensional nonlinear convection-diffusion equations based on gradient reconstruction

MIAO Jingjing, SUN Tongjun*   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2026-02-13

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Abstract: An adaptive finite element method is proposed for a class of two-dimensional nonlinear convection-diffusion equations. The characteristic method is used to deal with the convection term of the equation, and the numerical oscillation and numerical dispersion caused by the convection dominant are effectively solved. An adaptive finite element algorithm based on a posterior error estimates of gradient reconstructiontype is designed to further adjust the mesh and improve the precision on the basis of standard finite element method. Finally, numerical experiments are carried out to verify the effectiveness of the proposed method.

Key words: the nonlinear convection-diffusion equation, the characteristic method, gradient reconstruction, adaptive finite element method

CLC Number: 

  • O241
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