5 papers
Optimal convergence rates in for a first order system least squares finite element method -- Part II: inhomogeneous Robin boundary conditions
Maximilian Bernkopf, Jens Markus Melenk
We consider divergence-based high order discretizations of an -based first order system least squares formulation of a second order elliptic equation with Robin boundary condi…
Wavenumber-explicit stability and convergence analysis of hp finite element discretizations of Helmholtz problems in piecewise smooth media
M. Bernkopf, T. Chaumont-Frelet, J. M. Melenk
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…
Solvability of Discrete Helmholtz Equations
Maximilian Bernkopf, Stefan Sauter, Céline Torres +1
We study the unique solvability of the discretized Helmholtz problem with Robin boundary conditions using a conforming Galerkin -finite element method. Well-posedness of the di…
Optimal convergence rates in for a first order system least squares finite element method. Part I: homogeneous boundary conditions
Maximilian Bernkopf, Jens Markus Melenk
We analyze a divergence based first order system least squares method applied to a second order elliptic model problem with homogeneous boundary conditions. We prove optimal conver…
Analysis of the -version of a first order system least squares method for the Helmholtz equation
Maximilian Bernkopf, Jens Markus Melenk
Extending the wavenumber-explicit analysis of [Chen & Qiu, J. Comput. Appl. Math. 309 (2017)], we analyze the -convergence of a least squares method for the Helmholtz equation…