EFG Method Of Parabolic Partial Differential Equation And Error Estimate

Meshless method is one of the hot studies in numerical analysis by far both at home and abroad. And Element free Galerkin method is one of Meshless methods. In EFGM the shape function is constructed by the moving least square(MLS) approximation, and it makes use of the Galerkin method to get it's equal integral equation, then through deal with essential boundary conditions and gets the Galerkin weak form of differential equation.Firstly, the paper systematically introduces the background knowledge and present development of meshless method and it's advantages. Detaily introduces the basic theory of EFGM. This part mainly give a presentation of the moving least square approximation, the methods of dealing with boundary conditions, integral schemes.Secondly, point out that meshless method is different from finite element method in handling boundary condition and numerical integral because the approximation function of meshless method is not inserted function, it have itself special methods. Deduces meshless Galerkin essential equation of parabolic partial differential equation with the method ofweighted residuals------Galerkin. Furthermore, discusses the main factors which may effectthe calculation precision and give some suggestion with which can get the best result.Thirdly, on the base of the existent error estimate of elliptical Galerkin projection operator, obtain semi-discrete and complete-discrete error estimates betwent EFG solution and exact solution of parabolic partial differential equation. Semi-discrete error estimate show that the rank of r is accordance with the approximation rank of subspace S_h. Complete-discrete error estimates show that it not only have relation with radius r of domain of influence, but also have relation with the step length of time variable and the way of discrete.Lastly, give typical examples and draw up procedures of MATLAB. The calculation shows EFG method have many virtues, such as, the correctness and high precision, the disposal is convenient before and after solve problem and so on.