Journal of Computational and Applied Mathematics
Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
Journal of Computational Physics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
Journal of Computational Physics
An ultra-weak method for acoustic fluid-solid interaction
Journal of Computational and Applied Mathematics
The Trefftz method for the Helmholtz equation with degeneracy
Applied Numerical Mathematics
Advances in Engineering Software
Journal of Computational and Applied Mathematics
A Compact Fourth Order Scheme for the Helmholtz Equation in Polar Coordinates
Journal of Scientific Computing
Journal of Computational Physics
Multi-domain Fourier-continuation/WENO hybrid solver for conservation laws
Journal of Computational Physics
A stable discontinuous Galerkin-type method for solving efficiently Helmholtz problems
Computers and Structures
An optimally blended finite-spectral element scheme with minimal dispersion for Maxwell equations
Journal of Computational Physics
Journal of Computational Physics
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The development of numerical methods for solving the Helmholtz equation, which behaves robustly with respect to the wave number, is a topic of vivid research. It was observed that the solution of the Galerkin finite element method (FEM) differs significantly from the best approximation with increasing wave number. Many attempts have been presented in the literature to eliminate this lack of robustness by various modifications of the classical Galerkin FEM.However, we will prove that, in two and more space dimensions, it is impossible to eliminate this so-called pollution effect. Furthermore, we will present a generalized FEM in one dimension which behaves robustly with respect to the wave number.