![]() ![]() They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering. Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions.- New RBF Collocation Methods and Kernel RBF. ![]() The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both. A new numerical method, which is based on the coupling between semi-Lagrangian (SL) method and element free Galerkin (EFG) method, is developed for convectiondiffusion partial differential equations with dominated convection terms. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain. ![]() Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. ![]()
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