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In this paper we study the -version of the Partition of Unity Method for the Helmholtz equation. The method is obtained by employing the standard bilinear finite element basis on a mesh of quadrilaterals discretizing the domain as the Partition of Unity used to paste together local bases of special wave-functions employed at the mesh vertices. The main topic of the paper is the comparison of the performance of the method for two choices of local basis functions, namely a) plane-waves, and b) wave-bands....
We deal with the a-posteriori estimation of the error for finite element solutions of nonstationary heat conduction problems with mixed boundary conditions on bounded polygonal domains. The a-posteriori error estimates are constucted by solving stationary “reconstruction” problems, obtained by replacing the time derivative of the exact solution by the time derivative of the finite element solution. The main result is that the reconstructed solutions, or reconstructions, are superconvergent approximations...
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