FINITE ELEMENT METHODS BASED ON GENERALIZED EXPO-RATIONAL B-SPLINES WITH HARMONIC POLYNOMIAL COEFFICIENTS

We present an upgrade of a recent work [7] where the performance of several novel Partition of Unity Methods (PUM) [2] were examined on non-degenerate triangulations for solving linear elliptic partial differential equations. The current study focuses on changing the local polynomials as functional coefficients in the Partition of Unity Methods (PUM) from Taylor expanding polynomials to harmonic polynomials. We provide numerical results to illustrate the behavior of the PUM when switching from local Taylor polynomials to local harmonic polynomials. These results support the conclusion that on sufficiently refined meshes harmonic polynomials tend to outperform Taylor polynomials. AMS Subject Classification: 65N30, 65N38, 31A05