Analysis of the $hp$-version of a first order system least squares method for the Helmholtz equation
Provides refined error bounds for the hp-version of a least squares method for the Helmholtz equation, benefiting computational scientists solving high-frequency wave problems.
The paper analyzes the L^2-convergence of a least squares method for the Helmholtz equation, obtaining improved rates in mesh size h and polynomial degree p under specific conditions on hk/p and p/log k.
Extending the wavenumber-explicit analysis of [Chen & Qiu, J. Comput. Appl. Math. 309 (2017)], we analyze the $L^2$-convergence of a least squares method for the Helmholtz equation with wavenumber $k$. For domains with an analytic boundary, we obtain improved rates in the mesh size $h$ and the polynomial degree $p$ under the scale resolution condition that $hk/p$ is sufficiently small and $p/\log k$ is sufficiently large.