Geodesic
A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation
Applications of Mathematics, Tome 61 (2016) no. 1, pp. 27-45.

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In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers' equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the $P_0^2-P_1$ pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.
DOI : 10.1007/s10492-016-0120-3
Classification : 35Q30, 65B05, 65N12, 65N30
Keywords: Burgers' equation; mixed finite element method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition 
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     title = {A new mixed finite element method based on the {Crank-Nicolson} scheme for {Burgers'} equation},
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Hu, Xiaohui; Huang, Pengzhan; Feng, Xinlong. A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation. Applications of Mathematics, Tome 61 (2016) no. 1, pp. 27-45. doi : 10.1007/s10492-016-0120-3. http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0120-3/

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