Point Value and Point Load Boundary Conditions
POINT VALUE boundary conditions can be added by placing
POINT VALUE ( variable ) = expression
following a coordinate specification. The stated value will be imposed at the coordinate point immediately preceding the specification.
POINT LOAD boundary conditions can be added by placing
POINT LOAD ( variable ) = expression
following a coordinate specification. The stated load will be imposed as a lumped source on the coordinate point immediately preceding the specification.
The results achieved by use of these specifications are frequently disappointing.
A diffusion equation, for example, div(grad(u))+s=0, can support solutions of the form u=A-Br-Cr^2, where r is the distance from the point value and A, B and C are arbitrary constants. By the superposition principle, FlexPDE is free to add such shapes to the computed solution in the vicinity of the point value, without violating the PDE. A POINT VALUE condition usually leads to a sharp spike in the solution, pulling the value up to that specified, but otherwise leaving the solution unmodified.
The POINT LOAD is not subject to this same argument, but since it is a load without scale, it will frequently produce a dense mesh refinement around the point.
A better solution is to use a distributed load or an extended value boundary segment, ring or box.