Small data oscillation implies the saturation assumption
The saturation assumption asserts that the best approximation error in \(H_0^1\) with piecewise quadratic finite elements is strictly smaller than that of piecewise linear finite elements. The main result in this paper states that the saturation assumption holds provided the data oscillation is controlled by the approximation error with linear finite elements. The technique used by the authors comes from a posteriori error analysis.
scientific article; zbMATH DE number 1747961