Operator adapted spectral element methods. I: Harmonic and generalized harmonic polynomials
The approximation of elliptic differential equations by operator adapted spectral elements is investigated. The adapted systems have superior local approximation properties. The approximation by harmonic polynomials is studied for equations with the Laplace operator. Special attention is paid to the approximation of singular functions that arise in corners. By the theory of Bergman and Vekua the results are extended to general elliptic problems. The partition of unity is used in a numerical example.
operator adapted spectral element methods
scientific article; zbMATH DE number 1398747