The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the proceedings papers of the Fourth International Workshop on Meshfree Methods held in September 2007 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this very active and exciting area of interdisciplinary research and to present recent advances and results in this field.

Zusammenfassung
The Fourth International Workshop on Meshfree Methods for Partial D- ferential Equations was held from September 17 to September 20, 2007 in Bonn, Germany. One of the major goals of this workshop series is to bring together European, American and Asian researchers working in this exciting ?eld of interdisciplinary research on a regular basis. To this end Ivo Babu? ska, Ted Belytschko, Michael Griebel, Antonio Huerta, Wing Kam Liu, and Harry Yserentant invited scientist from twelve countries to Bonn to strengthen the mathematical understanding and analysis of meshfree discretizations but also to promote the exchange of ideas on their implementation and application. The workshop was again hosted by the Institut fur ¨ Numerische Simu- tionattheRheinischeFriedrich-Wilhelms-Universit¨ atBonnwiththe?nancial support of the Sonderforschungsbereich 611 Singular Phenomena and Scaling in Mathematical Models. This volume of LNCSE now comprises selected contributions of attendees of the workshop. Their content ranges from applied mathematics to physics and engineering. This is also an indication that meshfree methods for the numerical solution of partial di?erential equations are becoming more and more mainstream in many areas of applications due to their ?exiblity and wide applicability.

Inhalt
Circumventing Curse of Dimensionality in the Solution of Highly Multidimensional Models Encountered in Quantum Mechanics Using Meshfree Finite Sums Decomposition.- A Pressure Correction Approach Coupled with the MLPG Method for the Solution of the Navier-Stokes Equations.- Large Scale, Multiresolution Flow Simulations Using Remeshed Particle Methods.- On the Stabilization of Stress-Point Integration in the Element Free Galerkin Method.- The Partition of Unity Meshfree Method for Solving Transport-Reaction Equations on Complex Domains: Implementation and Applications in the Life Sciences.- Solving One Dimensional Scalar Conservation Laws by Particle Management.- Stability of Energy Transfer in the Weak Coupling Method.- Multiscale Approach for Quantum Systems.- A Meshless Technique Based on Integrated Radial Basis Function Networks for Elliptic Partial Differential Equations.- A Higher-Order Finite Volume Method Using Multiresolution Reproducing Kernels.- Interface Tracking in Meshfree Methods and its Applications.- A'posteriori Error Estimation Based on Higher Order Approximation in the Meshless Finite Difference Method.- Exact Bounds for Linear Outputs of the Convection-Diffusion-Reaction Equation Using Flux-Free Error Estimates.- Preparation of CAD and Molecular Surfaces for Meshfree Solvers.- 3D Meshfree Magnetohydrodynamics.- A Particle-Partition of Unity Method Part VIII: Hierarchical Enrichment.- A Framework For Studying The RKEM Representation of Discrete Point Sets.- Coupling of the CFD and the Droplet Population Balance Equation with the Finite Pointset Method.- Hybrid Methods for Fluid-Structure-Interaction Problems in Aeroelasticity.