Based on the weighted-residual error estimator from , we introduced an overall error estimator which controls both, the discretization error
as well as the data approximation error (Theorem 3.
In this research, the discretization error
was caused by the formulation of the FDTD method, and the round-off error was caused by continuously rounding off the digits during the simulation.
Exploring Discretization Error
in Simulation-Based Aerodynamic Databases
Corresponding discretization error
estimates can be found in ; the case [alpha] = 0 is considered in Deckelnick, Hinze .
The main result of the space discretization error
analysis for the time-harmonic eddy current optimal control problem is summarized in the next theorem.
The following lemma provides an abstract estimate for the discretization error
in the mesh-dependent norm [?
As we have pointed out, the discretization error
due to the replacement of the integral with the first infinite summation is approximately equal to exp(-2[pi]d/N), while the truncation error due to the truncation of the first infinite summation from the Definition 2.
We prove that the discretization error
is small uniformly with respect to [epsilon] in a subregion [[OMEGA].
Unfortunately, a balance of the truncation and discretization error
cannot be maintained.
In , under certain assumptions, an estimate of the total discretization error
is derived, stating that if [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] then for all [t.
a solution of the continuous problem that is only disturbed by the discretization error
Notice the expected stagnation of the error around the size of the Finite Element discretization error