A Numerical Analysis Of The Circulation Of Magnetic Convection In Celestial Bodies By The Finite Element Method

In this thesis,we mainly study the finite element method of celestial magnetic prob-lems in different regions,and obtain some super-convergent results by using the two grid method,the two level method and the post-processing technology.At the same time,we make a theoretical correction to the incomplete results.In the first part,the two grid method(TGM)and the two level method(TLM)are used to solve the convection diffusion problem in the convection region,respectively.Specifically,Under the two grid method,with the help of the existing high-precision results,the average value technique and the interpolation post-processing technology,The super approximation estimates and global convergence results in the sense of H1 norm with order O(?2+h+H2)are obtained in the Crank-Nicson fully discrete scheme,(where h,H and? are fine and coarse space step and time step).In the two-level method,using Q1 and Q2 elements,the convergence order in the sense of H1 norm of O(?2+h2)is obtained.At the same time,the corresponding numerical examples are given to verify the correctness of the theoretical analysis and the effectiveness of the method.In the second part,in the circulation area,we use the two grid method to explore the circulation problem in three-dimensional space.Specifically,similar to the analysis technique in the first part,with the help of the existing high-precision results,average technique and interpolation post-processing technique,we use the Nedelec element to theoretically obtain the backward Euler fully discrete scheme.The super-close estimates and global super convergence results of order O(?2+ h2+H5/2)In the third part,the author corrects the result that original literature not full on the convection circulation problem.The order(?+h2/3 in the original theorem is increased to(?+h1),Specifically,the Scott-Zhang operator is replaced by Ih operator.and the order is full by using the interpolation operator Ih.