The Study Of Decomposition Algorithm Based On Maximum Principle For Singularly Perturbed Problems

The derivative of the solutions, which is calculated from the finite element di-rectly, is not continuous and the overall accuracy is not high.However, we can use the postprocessing technique of the finite element to get a high convergence order of the derivative than the usual one.In this paper, with respect to the two-point boundary value problem of second-order differential equations, we succeed in ob-taining a global accuracy by using the finite element postprocessing technique on the basis of some superconvergence.We known that the derivative of the linear finite element solutions can get the convergence accuracy order of 1 in global interval. This paper create a new method, that is, we can use the postprocessing technique to get the convergence accuracy order of 2 in global interval, basing on the original numerical result.The specific process is as follows:firstly, we plot the global interval, and use the linear finite element method to get the values of the nodes;secondly, we go on solving the equations with linear and quadratic element respectively to get the value of the midpoint in every subinterval(therefore a nod is added). Some numerical result show that the two methods we use can both improve the overall accuracy of the derivative effectively.