Simulation of the Solution of a Viscous Porous Medium Equation by a Particle Method

To solve a particular partial differential equation, namely a viscous porous medium equation, we discuss a particle method, which is based on the concept of moderately interacting many-particle systems. Our approach may be classified as a combination of a smoothed particle hydrodynamics method and a particle-mesh method. Quantitatively, it is assessed in terms of estimates on the approximation error.

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