Contributions to Books:
S. Esterhazy, J. Melenk:
"On Stability of Discretizations of the Helmholtz Equation";
in: "Numerical Analysis of Multiscale Problems",
We reviewthe stability properties of several discretizations of the Helmholtz
equation at large wavenumbers. For a model problem in a polygon, a complete kexplicit
stability (including k-explicit stability of the continuous problem) and convergence
theory for high order finite element methods is developed. In particular,
quasi-optimality is shown for a fixed number of degrees of freedom per wavelength
if the mesh size h and the approximation order p are selected such that kh/p is sufficiently
small and p = O(logk), and, additionally, appropriate mesh refinement is
used near the vertices. We also review the stability properties of two classes of numerical
schemes that use piecewise solutions of the homogeneous Helmholtz equation,
namely, Least Squares methods and Discontinuous Galerkin (DG) methods.
The latter includes the Ultra Weak Variational Formulation.
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
Created from the Publication Database of the Vienna University of Technology.