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This allows a reliable estimation of the solution error.
Assessing solution error continues to be a formidable task when numerically solving practical flow problems.
The equation relating the optimal solution error and the errors of the input data is used to construct an approximation of the optimal solution error covariance.
It is shown that either way, solution error is second order in the mesh spacing.
In Figure 2, we show the profiles of the exact solution u alongside the solution error.
Significant accuracy gains in manufactured solution error norms are noted even with modest promotion of the underlying polynomial order.
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The effect of parameter errors and optimality tolerances in solution algorithms on solution errors are studied.
The dependence of the solution errors on the discretization errors is analyzed in certain flow cases.
It also shows that the model solution errors are similar for an optimality tolerance of within 4%.
Model errors, which include numerical solution errors and model form errors, are quantified through Gaussian process models and included in the reliability analysis.
During this time interval, the LSE may have a mismatch between measurement and model, which can create significant solution errors.
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