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I am attempting to use the method of manufactured solutions (MMS) for code verification for linear elasticity. However, this is more of a general question regarding the general use of MMS.

In MMS, the manufacturer makes up some solution that satisfies the PDE, and then we obtain values for BCs and sources that we feed into the numerical code and solve. Does the manufacturer have the freedom in choosing whether a boundary is a Dirichlet or Neumann boundary condition, and then evaluating the manufactured solution at the boundary in accordance with their choice of the boundary condition type?

For example, in 1-D steady heat-conduction, I manufacture some solution $T(x)$. Do I have the freedom of using either Dirichlet BC at $x=0$ or Neumann BC? For a Dirichlet BC, I simply evaluate $T(x)$ at $x=0$ and that's my BC. On the other hand, I could instead use a Neumann BC at $x=0$ so I would then evaluate $\frac{dT}{dx}$ at $x=0$. Is the manufacturer in full of control of what type of BC is to be prescribed?

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  • $\begingroup$ Yes, as long you choose a set of bc that leads to a well-posed problem. $\endgroup$ – cpraveen Apr 29 '18 at 5:13
  • $\begingroup$ Is it possible to manufacture solutions that yield the same boundary conditions for transient problems? If this possible, I assume it implies that the problem is not well posed since the BC does not lead to a unique solution? $\endgroup$ – user27504 Apr 29 '18 at 15:28

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