Re:Introduction to Position Based Fluids
by noname123 on Wednesday April 24, 2013 @12:13PM
(#5602275)
Is finite element method good enough? Can you provide a concrete example where approximation is not good enough.
Re:Introduction to Position Based Fluids
by coherentpony on Wednesday April 24, 2013 @02:19PM
(#5603076)
Special approximations called 'Galerkin approximations' converge.
Finite element methods are a special case of Galerkin methods. Finite element methods are good enough.
Non-trivial closed-form solutions are hopeless. Existence of solutions is a little less hopeless. Existence of solutions over small time horizons has been proven. This is all in three space dimensions.
There is a theorem stating that if global-time solutions exist and are unique, then computationally computed approximate solutions are 'good'. Moreover, they get better as you refine the computational domain.