I think I am quite confused by the nuance of meshfree methods https://en.wikipedia.org/wiki/Meshfree_methods for solving some PDE over $\Omega$. From what I gather they do not require the discretisation of $\Omega$. Therefore if say $\Omega$ was very high dimensional, would these methods avoid the curse of dimensionality - or does that still come into play somewhere ?
I'm thinking of the Heat Equation $\partial_t\rho=\Delta \rho$, and comparing the finite difference method to say an Euler Maruyama method (which I assume is meshfree).
