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I am trying to solve a system of partial differential equations over a cube region. The text is as follows:

<< NDSolve`FEM`
\[Beta] = 
 Parallelepiped[{-1, -1, -1}, {{0, 0, 2}, {2, 0, 0}, {0, 2, 0}}]
mesh = ToBoundaryMesh[\[Beta]]
mesh2 := ToElementMesh[mesh, MaxCellMeasure -> 0.01]
J = 10;
w = 1;
Y = 10;
{Asol, Bsol, psol} = 
 NDSolveValue[{D[A[x, y, z], z] - D[p[x, y, z], x] == 0, 
   D[p[x, y, z], y] - D[B[x, y, z], z] == 0, 
   D[B[x, y, z], x] - D[A[x, y, z], y] == 1, 
   DirichletCondition[p[x, y, z] == 0, z == -1], 
   DirichletCondition[p[x, y, z] == 0, z == 1], 
   DirichletCondition[B[x, y, z] == 0, y == -1], 
   DirichletCondition[A[x, y, z] == 0, x == -1], 
   DirichletCondition[A[x, y, z] == 0, x == 1], 
   DirichletCondition[B[x, y, z] == 0, y == 1]}, {A, B, 
   p}, {x, y, z} \[Element] mesh2]

Everything seems to work fine, however, when I evaluate the value of D[B[x, y, z], x] - D[A[x, y, z], y] at any point, I am returned with 0, which does not match the equation that I entered, that estipulates that D[B[x, y, z], x] - D[A[x, y, z], y] == 1. So essentialy, mathematica is returning me a solution to my system of PDEs that doesn't actually solve the system. How can I fix this ? Code image

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  • $\begingroup$ The solution of the system of equations diverges. The task is incorrectly set. $\endgroup$ – Alex Trounev Nov 13 '18 at 22:38

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