A Meshless Solution to the p-Laplace Equation
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.
Keywordsp-Laplace Non-linear methods Kansa Method
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