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We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
In this article, we analyze a two-level finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse…
Stabilised mixed velocity-pressure formulations are one of the widely-used finite element schemes for computing the numerical solutions of laminar incompressible Navier-Stokes. In these formulations, the Newton-Raphson scheme is employed to…
We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…
We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the space--time formulation of the Navier--Stokes…
We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…
A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…
This paper presents an enriched Galerkin (EG) finite element method for the incompressible Navier--Stokes equations. The method augments continuous piecewise linear velocity spaces with elementwise bubble functions, yielding a locally…
We present a space-time Cut Finite Element Method (CutFEM) for the time-dependent Navier-Stokes equations involving two immiscible incompressible fluids with different viscosities, densities, and with surface tension. The numerical method…
In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the…
We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wise mass conservation, energy stability, and pressure…
A new high order accurate staggered semi-implicit space-time discontinuous Galerkin (DG) method is presented for the simulation of viscous incompressible flows on unstructured triangular grids in two space dimensions. The staggered DG…
In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…
In this work, a multirate in time approach resolving the different time scales of a convection-dominated transport and coupled fluid flow is developed and studied in view of goal-oriented error control by means of the Dual Weighted Residual…
We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier--Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is…
We model incompressible flows with an adaptive stabilized finite element method Stokes flows, which solves a discretely stable saddle-point problem to approximate the velocity-pressure pair. Additionally, this saddle-point problem delivers…
This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…
Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…
We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…
In this paper, an error analysis of a three steps two level Galekin finite element method for the two dimensional transient Navier-Stokes equations is discussed. First of all, the problem is discretized in spatial direction by employing…