Oscillation in a posteriori error estimation
For numerical analysts and engineers using finite element methods, this provides a more reliable error estimator by resolving the long-standing oscillation problem.
The paper introduces a new approach to a posteriori error estimation that ensures oscillation terms are dominated by the error and capture unquantifiable residual parts, achieving stability regardless of mesh fineness or solution regularity.
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the following two properties. First, it is dominated by the error, irrespective of mesh fineness and the regularity of data and the exact solution. Second, it captures in terms of data the part of the residual that, in general, cannot be quantified with finite information. The new twist in our approach is a locally stable projection onto discretized residuals.