Meshfree Methods for Partial Differential Equations

1. Front Matter

   Pages I-IX

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2. Meshless and Generalized Finite Element Methods: A Survey of Some Major Results

   • I. Babuška, U. Banerjee, J. E. Osborn

   Pages 1-20

3. Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations

   • Jörn Behrens, Armin Iske, Martin Käser

   Pages 21-36

4. New Methods for Discontinuity and Crack Modeling in EFG

   • Ted Belytschko, Giulio Ventura, Jingxiao Xu

   Pages 37-50

5. SPH Simulations of MHD Shocks Using a Piecewise Constant Smoothing Length Profile

   • Steinar Børve, Marianne Omang, Jan Trulsen

   Pages 51-62

6. On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions

   • Ismail Boztosun, Abdellatif Charafi, Dervis Boztosun

   Pages 63-73

7. New RBF Collocation Methods and Kernel RBF with Applications

   • Wen Chen

   Pages 75-86

8. Tuned Local Regression Estimators for the Numerical Solution of Differential Equations

   • Gary A. Dilts, Aamer Haque, John Wallin

   Pages 87-104

9. Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights

   • Gregory E. Fasshauer

   Pages 105-116

10. Coupling Finite Elements and Particles for Adaptivity: An Application to Consistently Stabilized Convection-Diffusion

    • Sonia Fernández-Méndez, Antonio Huerta

    Pages 117-129

11. A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations

    • Jason Frank, Georg Gottwald, Sebastian Reich

    Pages 131-142

12. Fast Multi-Level Meshless Methods Based on the Implicit Use of Radial Basis Functions

    • Csaba Gáspár

    Pages 143-160

13. A Particle-Partition of Unity Method-Part IV: Parallelization

    • Michael Griebel, Marc Alexander Schweitzer

    Pages 161-192

14. Some Studies of the Reproducing Kernel Particle Method

    • Weimin Han, Xueping Meng

    Pages 193-210

15. Consistency by Coefficient-Correction in the Finite-Volume-Particle Method

    • Dietmar Hietel, Rainer Keck

    Pages 211-221

16. Do Finite Volume Methods Need a Mesh?

    • Michael Junk

    Pages 223-238

17. An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations

    • Jörg Kuhnert

    Pages 239-249

18. Adaptive Galerkin Particle Method

    • Hongsheng Lu, Jiun-Shyan Chen

    Pages 251-265

19. An Adaptivity Procedure Based on the Gradient of Strain Energy Density and its Application in Meshless Methods

    • Yunhua Luo, Ulrich Häussler-Combe

    Pages 267-279

20. New Developments in Smoothed Particle Hydrodynamics

    • Joseph J. Monaghan

    Pages 281-290

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. 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 of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

• Regression
• Simulation
• differential equation
• element-free Galerkin methodse
• engineering applications
• finite element method
• finite elements
• meshfree discretizations
• modeling
• partial differential equations
• partition of united method
• reproducing kernel particle methods
• smoothed particle hydrodynamics
• stability
• stochastic particle methods

• Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

  Michael Griebel, Marc Alexander Schweitzer

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