A Meshless Solution to the p-Laplace Equation

  • Francisco Manuel Bernal Martinez
  • Manuel Segura Kindelan
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 11)

The p-Laplace equation is a non-linear elliptic PDE which plays an important role in the modeling of many phenomena in areas such as glaciology, non-Newtonian rheology or edge-preserving image deblurring. We have linearized it and applied a scheme introduced by G. Fasshauer which allows to solve it in the framework of Kansa's method. In order to confirm the validity of the approach, a 2D example (the pressure distribution in Hele-Shaw flow) has been numerically solved. The convergence and accuracy of the method are discussed, and an improvement based on smoothing up the linearized PDE is suggested.


p-Laplace Non-linear methods Kansa Method 


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Copyright information

© Springer Science + Business Media B.V 2009

Authors and Affiliations

  • Francisco Manuel Bernal Martinez
    • 1
  • Manuel Segura Kindelan
    • 1
  1. 1.G. Millán Institute for Modeling, Simulation and Industrial MathematicsUniversidad Carlos III de MadridLeganés

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