An analysis of discretizations of the Helmholtz equation in L-2 and in negative norms

作者：Esterhazy S; Melenk J M^*

来源：Computers & Mathematics with Applications, 2014, 67(4): 830-853.

DOI：10.1016/j.camwa.2013.10.005

• Helmholtz equation
• High order FEM
• Dispersion error
• Regularity

For a model Helmholtz problem at high wavenumber k we present a wavenumber-explicit error analysis in the L-2-and H-1-norms for the Galerkin FEM. For the convergence in L-2, we show that the lowest order case p = 1 is special in that the relative error in L-2 scales at best with k whereas it does not for higher order discretizations. An alternative to the Galerkin method with better dispersion properties is the optimally blended spectral finite element scheme of Ainsworth and Wajid (2010). For this method, we present an error analysis in L2 for the lowest order case p = 1 in one dimension, showing that the L-2-error is improved by a factor k compared to the lowest order Galerkin FEM.

• 出版日期2014-3