Monte Carlo approximations of the Neumann problem

Details Monte Carlo approximations of the Neumann problem Monte Carlo approximations of the Neumann problem

2012-03-22

arxiv.org/abs/1203.4910v1

Mathematics

Probability

Soumis (2012)

Scientific paper

We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the invariant measure of the stochastic process associated to the equation. Pointwise approximations are computed by means of standard and new simulation schemes especially devised for local time approximation on the boundary of the domain. Global approximations are computed thanks to a stochastic spectral formulation taking into account the property of zero mean value of the solution. This stochastic formulation is asymptotically perfect in terms of conditioning. Numerical examples are given on the Laplace operator on a square domain with both pure Neumann and mixed Dirichlet-Neumann boundary conditions.

Affiliated with

Also associated with

No associations

Rating

Monte Carlo approximations of the Neumann problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Monte Carlo approximations of the Neumann problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Monte Carlo approximations of the Neumann problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-381450