PUMA publications for /group/simtech/DensityMon Mar 27 10:59:39 CEST 2023Ann. Mat. Pura Appl. (4)51923--1959Stratified periodic water waves with singular density gradients1992020Lienstromberg gradients singular density The authors consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is bounded from below by an impermeable horizontal bed. Three equivalent classical formulations in a suitable setting of strong solutions which may describe nevertheless waves with singular density gradients are established. The availability of a weak formulation of the water wave problem, the regularity properties of the corresponding weak solutions, and methods from nonlinear functional analysis are used. The paper is organized as follows. In Section 2, the three formulations of the problem are introduced and their equivalence is established. In Section 3, the authors first introduce the notion of a weak solution to Dubreil-Jacotin's formulation and establish, by means of a shooting method, the existence of at least one laminar flow solution to this latter formulation. In Section 4, the equations are reformulated as an abstract bifurcation problem by using methods from nonlinear functional analysis.Fri Jul 20 10:54:15 CEST 2018Theoretical and Computational Fluid Dynamics1-20{Comparison of dynamical cores for NWP models: comparison of COSMO and Dune}2012Finite Density Discontinuous differences; Compressible current; Euler; gravity Navier???Stokes; Galerkin; Inertia flow; vorlaeufig Fri Jul 20 10:54:15 CEST 2018IMA Journal of Numerical Analysis3947-970A Convergence Proof for Adaptive Finite Elements without Lower Bound312011adaptivity convergence elements finite density vorlaeufig We analyse the adaptive finite-element approximation to solutions of partial differential equations in variational formulation. Assuming well-posedness of the continuous problem and requiring only basic properties of the adaptive algorithm, we prove convergence of the sequence of discrete solutions to the true one. The proof is based on the ideas by Morin, Siebert and Veeser but replaces local efficiency of the estimator by a local density property of the adaptively generated finite-element spaces. As a result, estimators without a discrete lower bound are also included in our theory. The assumptions of the presented framework are fulfilled by a large class of important applications, estimators and adaptive strategies.