Journal of Computational Physics
Computational aspects of the ultra-weak variational formulation
Journal of Computational Physics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Integration pointwise pollution error estimates in the finite element method in one dimension
Applied Numerical Mathematics
A fourth-order Magnus scheme for Helmholtz equation
Journal of Computational and Applied Mathematics
Finite Elements in Analysis and Design
Iterative solvers for coupled fluid-solid scattering
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Analysis of one-dimensional Helmholtz equation with PML boundary
Journal of Computational and Applied Mathematics
Controllability method for the Helmholtz equation with higher-order discretizations
Journal of Computational Physics
Discontinuous Galerkin methods with plane waves for time-harmonic problems
Journal of Computational Physics
The Trefftz method for the Helmholtz equation with degeneracy
Applied Numerical Mathematics
Finite Elements in Analysis and Design
Structural and Multidisciplinary Optimization
Wavenumber Explicit Convergence Analysis for Galerkin Discretizations of the Helmholtz Equation
SIAM Journal on Numerical Analysis
WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit
SIAM Journal on Numerical Analysis
A finite element method enriched for wave propagation problems
Computers and Structures
An optimally blended finite-spectral element scheme with minimal dispersion for Maxwell equations
Journal of Computational Physics
Overlapping solution finite element method - Higher order approximation and implementation
Applied Numerical Mathematics
Error Estimates of the Finite Element Method for Interior Transmission Problems
Journal of Scientific Computing
General DG-Methods for Highly Indefinite Helmholtz Problems
Journal of Scientific Computing
An analysis of discretizations of the Helmholtz equation in L2 and in negative norms
Computers & Mathematics with Applications
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In this paper, which is part II in a series of two, the investigation of the Galerkin finite element solution to the Helmholtz equation is continued. While part I contained results on the $h$ version with piecewise linear approximation, the present part deals with approximation spaces of order $p \ge 1$. As in part I, the results are presented on a one-dimensional model problem with Dirichlet--Robin boundary conditions. In particular, there are proven stability estimates, both with respect to data of higher regularity and data that is bounded in lower norms. The estimates are shown both for the continuous and the discrete spaces under consideration. Further, there is proven a result on the phase difference between the exact and the Galerkin finite element solutions for arbitrary $p$ that had been previously conjectured from numerical experiments. These results and further preparatory statements are then employed to show error estimates for the Galerkin finite element method (FEM). It becomes evident that the error estimate for higher approximation can---with certain assumptions on the data---be written in the same form as the piecewise linear case, namely, as the sum of the error of best approximation plus a pollution term that is of the order of the phase difference. The paper is concluded with a numerical evaluation.