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Keywords:
Burgers' equation; mixed finite element method; stable conforming finite element; Crank-Nicolson scheme; inf-sup condition
Summary:
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.
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