Fourth order eigenvalue approximation by extrapolation on domains with reentrant corners (Q910172)

The eigenvalue problem of the Laplace operator is considered on a non- convex domain composed of rectangles. This model problem may be solved by the finite element method with bilinear elements on a rectangular mesh. It is shown that, if the mesh has \(O(h^{-2})\) points and is appropriately graded, then a simple extrapolation scheme increases the accuracy from \(O(h^{2\beta})\) to \(O(h^{2q\beta})\), where \(\leq \beta <1\), q is the grading parameter which may make 2q\(\beta\) to be 4.