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p -> k in verification description
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danshapero committed Jun 28, 2024
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Expand Up @@ -373,8 +373,8 @@ \subsection{Verification on solvable test cases}

The verification exercises we use are taken from those used to test the implementation of the primal form of SSA in the icepack package\citep{shapero2021icepack}.
We compare numerical results on a sequence of grids to exactly solvable instances of SSA and check that the results converge with the expected order of accuracy.
Finite element theory predicts that the $L^2$-norm difference between the exact solution and the solutions obtained using $CG(k)$ finite elements is $\mathscr{O}(\delta x^{p + 1})$ where $\delta x$ is the mesh spacing.
If the slope in a log-log fit of error against mesh spacing deviates significantly from $p + 1$, this would indicate some mis-specification of the problem or bug in the solver.
Finite element theory predicts that the $L^2$-norm difference between the exact solution and the solutions obtained using $CG(k)$ finite elements is $\mathscr{O}(\delta x^{k + 1})$ where $\delta x$ is the mesh spacing.
If the slope in a log-log fit of error against mesh spacing deviates significantly from $k + 1$, this would indicate some mis-specification of the problem or bug in the solver.

The first test is to use the exact solution for the velocity of a floating ice shelf with thickness
\begin{equation}
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