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partial differential equation
Posted 15 nov. 2023, 07:29 UTC−5 Mesh, Equation-Based Modeling 1 Reply
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How to specify the Neumann boundary conditions in a coefficient form partial differential equation? (The derivative of u specified by the constraint is affected by the size of the grid)
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If you use a sufficiently fine mesh and/or sufficiently high order discretization then you can usually successfully/correctly compute solutions that may have strong gradients (spatially or temporally) in their derivatives. Under those circumstances, the specification of u (or its derivative) on a boundary will not introduce a mesh-dependent effect. If you see a strong mesh dependent effect on your solution, then you need to either use a finer mesh, a higher-order discretization, or both. (And in time domain, you might need to take shorter time steps.) Note: if you are able/willing to describe a more specific math or physics problem, then you may possibly receive more useful/specific advice on this forum.
p.s. I'm assuming that by "grid" you are referring to the finite element mesh, or perhaps to size of steps in time. If you meant something else, then my answer may not apply.
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