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Analytic solution is incorrect
The analytic solution defined in fem/analytic_soln.hpp corresponds to a case where the internal heat source term Q is zero. In the miniapp code, however, the source term is set to 1 (Hex8::sourceVector: Scalar Q = 1.0;). Consequently, model error does not decrease as resolution is increased (e.g., absolute error at (0.5, 0.5, 0.5) is always between 0.05 and 0.06).
Fig. Comparison of analytic and numerical solutions on z==0.5 plane.