By using the finite element $p$-Version in convection-diffusion problems, we can attain to a stabilized and accurate results. Furthermore, the fundamental of the finite element $p$-Version is augmentation degrees of freedom. Based on the fact that the finite element and the meshless methods have similar concept, it is obvious that many ideas in the finite element can be easily used in the meshl...

The Finite Difference Method (FDM), within the framework of the Meshless Local PetrovGalerkin (MLPG) approach, is proposed in this paper for solving solid mechanics problems. A “mixed” interpolation scheme is adopted in the present implementation: the displacements, displacement gradients, and stresses are interpolated independently using identical MLS shape functions. The system of algebraic e...

A Meshless Local Petrov-Galerkin (MLPG) method has been developed for solving 3D elastodynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transien...

Meshless deformation based on shape matching is a new technique for simulating deformable objects which handles point-based objects and does not need connectivity information. The technique has been first presented in 2005 and is of interest to all fields which require fast, stable simulations which do not need to be physically correct. In particular the technique seems very suitable for use in...

The Moving Least Squares method (MLS) provides an approximation û of a function u based solely on values u(xj) of u on scattered ”meshless” nodes xj . Derivatives of u are usually approximated by derivatives of û. In contrast to this, we directly estimate derivatives of u from the data, without any detour via derivatives of û. This is a generalized Moving Least Squares technique, and we prove t...

1. Research Student, Department of Mechanical Engineering, School of Engineering, Gautam Buddha University, Greater Noida, Gautam Buddha Nagar, Uttar Pradesh, India 2. Assistant Professor, Department of Mechanical Engineering, School of Engineering, Gautam Buddha University, Greater Noida, Gautam Buddha Nagar, Uttar Pradesh, India; 3. Assistant Professor, Department of Mechanical Engineering, S...

In this work, the method of radial basis functions is used for finding the solution of an inverse problem with source control parameter. Because a much wider range of physical phenomena are modelled by nonclassical parabolic initial-boundary value problems, theoretical behavior and numerical approximation of these problems have been active areas of research. The radial basis functions (RBF) met...

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...