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3. DSS (Direct Stiffness Summation) is applied implicitly through the operators to ensure continuity of the solution at element boundaries and reduction of unnecessary multiplicity
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The example verifies the numerical solution by comparing it to the analytical solution:
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```math
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\begin{align}
@@ -268,8 +266,8 @@ Where $B$ applies boundary conditions to enforce $\boldsymbol{w} = 0$ at the dom
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This test case is set up in a vertical column domain from $z=0$ m to $z=30$ km with 30 vertical elements. The column is initialized with a decaying temperature profile, where:
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- The virtual temperature starts at $T_{virt\_surf} = 280$ K at the surface
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- It asymptotically approaches $T_{min\_ref} = 230$ K with height
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- The virtual temperature starts at $T_{\textrm{virt}\_\textrm{surf}} = 280$ K at the surface
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- It asymptotically approaches $T_{\textrm{min}\_\textrm{ref}} = 230$ K with height
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- The profile follows a hyperbolic tangent function with height
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- The pressure follows a hydrostatic balance equation
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- Density is calculated from the equation of state using virtual temperature and pressure
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