Meshless Method For Helmholtz Problem And Elliptic Variational Inequalities Problem

This thesis is composed of three sections.In section one, meshless method with radial basis functions(RBF) for Helrnholtzproblem is considered. By introducing various RBF, it yields the meshless method ofGalerkin type for the problem. Moreover, error estimates for the problem with the methodis derived. Then the numerical example is given and by comparing FEM, it discussed thenumerical precision and the effect of the parameter c in the RBF to its numerical solution.Finally, a method for selecting a good value for the parameter c in RBF is given.In section two, it introduces the point interpolation method combined radial basisfunctions with polynomial basis functions for the first and second kind of ellipticvariational inequalities(EVI)problem. Then error estimates for the problem is deduced.Using the Elasto-Plastic problem as an example, we conduct a discrete scheme, namely thecoupling of meshless method and Uzawa algorithm. Finally, the result for the numericalexample shows the coupling method is available and efficient.In section three, the moving least square for the first kind of elliptic variationalinequalities problem is discussed. The error estimates and the numerical example for theproblem are given respectively. The result shows that the method for the first kind ofelliptic variational inequalities problem has a high precision and is an efficient method.