139 research outputs found
A study of isogeometric analysis for scalar convection-diffusion equations
Isogeometric Analysis (IGA), in combination with the Streamline Upwind
Petrov--Galerkin (SUPG) stabilization, is studied for the discretization of
steady-state con\-vection-diffusion equations. Numerical results obtained for
the Hemker problem are compared with results computed with the SUPG finite element
method of the same order. Using an appropriate parameterization for IGA, the computed
solutions are much more accurate than those obtained with the finite element method,
both in terms of the size of spurious oscillations and of the sharpness of layers
Nonlinear Hyperbolic Problems: modeling, analysis, and numerics
The workshop gathered together
leading international experts, as well as most
promising young researchers, working on the modelling, the
mathematical analysis, and the numerical methods for nonlinear
hyperbolic partial differential equations (PDEs). The meeting focussed
on addressing outstanding issues and identifying promising new
directions in all three fields, i.e.
modelling, analysis, and numerical discretization.
Key questions settled around the lack of well-posedness theories for
multidimensional systems of conservation laws and the use of hyperbolic modelling beyond
the classical topic of gas dynamics. A focal point in numerics has been
the discretization of random evolutions and uncertainty quantification.
Equally important, new multi-scale methods and schemes for asymptotic regimes
have been considered
CutFEM and ghost stabilization techniques for higher order space-time discretizations of the Navier-Stokes equations
We propose and analyze computationally a new fictitious domain method, based
on higher order space-time finite element discretizations, for the simulation
of the nonstationary, incompressible Navier-Stokes equations on evolving
domains. The physical domain is embedded into a fixed computational mesh such
that arbitrary intersections of the moving domain's boundaries with the
background mesh occur. The potential of such cut finite element techniques for
higher order space-time finite element methods has rarely been studied in the
literature so far and deserves further elucidation. The key ingredients of the
approach are the weak formulation of Dirichlet boundary conditions by Nitsche's
method, the flexible and efficient integration over all types of intersections
of cells by moving boundaries and the spatial extension of the discrete
physical quantities to the entire computational background mesh including
fictitious (ghost) subdomains of fluid flow. Thereby, an expensive remeshing
and adaptation of the sparse matrix data structure are avoided and the
computations are accelerated. To prevent spurious oscillations caused by
irregular intersections of mesh cells, a penalization, defining also implicitly
the extension to ghost domains, is added. These techniques are embedded in an
arbitrary order, discontinuous Galerkin discretization of the time variable and
an inf-sup stable discretization of the spatial variables. The parallel
implementation of the matrix assembly is described. The optimal order
convergence properties of the algorithm are illustrated in a numerical
experiment for an evolving domain. The well-known 2d benchmark of flow around a
cylinder as well as flow around moving obstacles with arising cut cells and
fictitious domains are considered further
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