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We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument and a slowly
Externí odkaz:
http://arxiv.org/abs/2408.03587
In this paper, new representations of the Green`s function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2408.03108
Autor:
Melenk, J. M.1 (AUTHOR) melenk@tuwien.ac.at, Sauter, S. A.2 (AUTHOR) stas@math.uzh.ch
Publikováno v:
Foundations of Computational Mathematics. Dec2024, Vol. 24 Issue 6, p1871-1939. 69p.
Autor:
Sauter, S.
In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of polynomial order $k\geq1$ on conforming triangulations and discontinuous pressure approximations of order
Externí odkaz:
http://arxiv.org/abs/2204.01270
Autor:
Carstensen, C., Sauter, S.
The Crouzeix-Raviart triangular finite elements are $\inf$-$\sup$ stable for the Stokes equations for any mesh with at least one interior vertex. This result affirms a {\em conjecture of Crouzeix-Falk} from 1989 for $p=3$. Our proof applies to {\em a
Externí odkaz:
http://arxiv.org/abs/2105.14987
Autor:
Carstensen, C., Sauter, S.
In this paper, we prove that Crouzeix-Raviart finite elements of polynomial order $p\geq5$, $p$ odd, are inf-sup stable for the Stokes problem on triangulations. For $p\geq4$, $p$ even, the stability was proved by \'{A}. Baran and G. Stoyan in 2007 b
Externí odkaz:
http://arxiv.org/abs/2105.14981
Autor:
Graham, I. G., Sauter, S. A.
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an existence-uniqu
Externí odkaz:
http://arxiv.org/abs/1803.00966
We consider elliptic problems with complicated, discontinuous diffusion tensor $A_{\scriptscriptstyle 0} $. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say $A_{\varepsilon}$,
Externí odkaz:
http://arxiv.org/abs/1704.01890
Autor:
Carstensen, C., Sauter, S.
Publikováno v:
In Computers and Mathematics with Applications 15 February 2022 108:12-23
Publikováno v:
SIAM Journal on Mathematical Analysis; 2024, Vol. 56 Issue 5, p6232-6267, 36p