Solution Adaptive Mesh Using Moving Mesh Method

摘要

This work deals with mesh adaptation strategy to enhance the accuracy of numerical solution of partial differential equations.This was achieved economically by employing the Moving Grid Finite Difference Method.The method was reformulated as first order div-curl system.This system was then solved using the Least Square Finite Element method(LSFEM).The reformulation of the method has two desirable effects. Firstly,it eliminates the expensive gradient computation in the original method and secondly it allows the method to be employed for mesh adaptation with dynamic boundaries.A 2-D general finite element code implementing the mesh adaptation method based on LSFEM,capable of analyzing self-adjoint problems in elasticity and heat transfer with variety of boundary conditions,sources or sinks was developed and thoroughly validated.The code was used to analyze and adapt mesh for problems in heat transfer and elasticity.The method was found to perform satisfactorily in all test cases.