A Finite Element Method For Second-Order Elliptic Problems With Local Periodic Structure

The second-order elliptic problems with local periodic structure have been numerically solved and studied by means of the multi-scale finite element methods.Considering the classical the multi-scale asymptotic finite element methods haven’t paid enough attention to the classical boundary corrector factor,the numerical solutions on the boundary have got greater errors.Then combining the one-order approximative solutions of the elliptic problems and the numerical solutions of the boundary corrector factor,one obtains the numerical solutions whose errors of the strain and the stress on the boundary are very samll.Firstly,using the means of the multi-scale finite element methods,the one-order approximation’s numerical solutions of the second-order elliptic problems with local periodic structure has been obtained.Secondly,by the methods which divides densely on the boundary and coarsely in the domain,one obtains the approximation of the finite element solutions to the second-order elliptic problems.Finally,put the above solutions together the original problems’ numerical appromative solutions can be accquired.