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Solve an Elliptic PDE for u[x,y] with the rhs given by numerical f[u]?

POSTED BY: Maxim Lyutikov
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OK. Still, is there a way to solve elliptic equation with the numerically given right hand side?
POSTED BY: Maxim Lyutikov
POSTED BY: Gianluca Gorni

D[u[x, y], {x, 2}] + D[u[x, y], {y, 2}] == u[x, y]^(1.) is still a linear PDE, but Mathematica cannot handle it.

Yes, a related problem is NDSolve::femnonlinear: Nonlinear coefficients are not supported in this version of NDSolve.
POSTED BY: Maxim Lyutikov

Perhaps you meant u[x, y]^(1.) in the last equation, instead of u[x, y]^{1.}?

However, I think only linear F's are supported in the current version of NDSolve for pde. Try

NDSolve[{Laplacian[u[x, y], {x, y}] == u[x, y]^2, 
  DirichletCondition[u[x, y] == x + y, True]}, u, {x, y} \[Element] 
  Disk[]]
POSTED BY: Gianluca Gorni
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