Bernkopf, M., Chaumont-Frelet, T., & Melenk, J. M. (2025). Wavenumber-explicit stability and convergence analysis of ℎ𝑝 finite element discretizations of Helmholtz problems in piecewise smooth media. Mathematics of Computation, 94(351), 73–122. https://doi.org/10.1090/mcom/3958
Convergence; finite element methods; Helmholtz problems; high- frequency problems; high-order methods; stability
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Abstract:
We present a wavenumber-explicit convergence analysis of the hp Finite Element Method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber k. Our analysis covers the heterogeneous Helmholtz equation with Robin, exact Dirichlet-to-Neumann, and second order absorbing boundary conditions, as well as perfectly matched layers.
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Research Areas:
Mathematical and Algorithmic Foundations: 80% Modeling and Simulation: 20%
