On computing the pressure by the p version of the finite element method for Stokes problem.
On Conforming Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations.
On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow
The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite...
On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow
On dynamics of fluids in meteorology
We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl and others in the series of works on compressible, viscous and heat conducting fluids.
On Energy Inequality, Smoothness and Large Time Behavior in L2 for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
On equilibrium finite elements in three-dimensional case
The space of divergence-free functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements that have the same property. The easiest way of generating basis functions in these subspaces is considered.
On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations.
On evolution equations for moving domains.
On evolution Galerkin methods for the Maxwell and the linearized Euler equations
The subject of the paper is the derivation and analysis of evolution Galerkin schemes for the two dimensional Maxwell and linearized Euler equations. The aim is to construct a method which takes into account better the infinitely many directions of propagation of waves. To do this the initial function is evolved using the characteristic cone and then projected onto a finite element space. We derive the divergence-free property and estimate the dispersion relation as well. We present some numerical...
On evolution inequalities of a modified Navier-Stokes type. III
This is the last from a series of three papers dealing with variational equations of Navier-Stokes type. It is shown that the theoretical results from the preceding parts (existence and regularity of solutions) can be applied to the problem of motion of a fluid through a tube.
On evolution inequalities of a modified Navier-Stokes type. II
The present part of the paper continues the study of the abstract evolution inequality from the first part. Theorem 1 states the existence and uniqueness of a weak solution to the evolution inequality under consideration. The proof is based on the method of approximation of the weak solution by a sequence of strong solutions. Theorem 2 yields two regularity results for the strong solution.
On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions
In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity polynomially increasing with a scalar quantity that evolves according to an evolutionary convection diffusion equation with the right hand side that is merely -integrable over space and time. We also formulate a conjecture concerning regularity...
On exact controllability for the Navier-Stokes equations
On exact controllability for the Navier-Stokes equations
We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain with control distributed in an arbitrary fixed subdomain. The result that we obtain in this paper is as follows. Suppose that we have a given stationary point of the Navier-Stokes equations and our initial condition is sufficiently close to it. Then there exists a locally distributed control such that in a given moment of time the solution of the Navier-Stokes...
On existence and regularity of solutions to a class of generalized stationary Stokes problem
We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the “pressure” gradient is replaced by a linear operator of first order.
On existence and Schauder regularity of solutions to a class of generalized stationary Stokes problems
On existence of a boundary layer near a three-phase contact point.
On existence of solutions for the nonstationary Stokes system with boundary slip conditions
Existence of solutions for equations of the nonstationary Stokes system in a bounded domain Ω ⊂ ℝ³ is proved in a class such that velocity belongs to , and pressure belongs to for p > 3. The proof is divided into three steps. First, the existence of solutions with vanishing initial data is proved in a half-space by applying the Marcinkiewicz multiplier theorem. Next, we prove the existence of weak solutions in a bounded domain and then we regularize them. Finally, the problem with nonvanishing...
On finite element approximation of flow induced vibration of elastic structure
In this paper the fluid-structure interaction problem is studied on a simplified model of the human vocal fold. The problem is mathematically described and the arbitrary Lagrangian-Eulerian method is applied in order to treat the time dependent computational domain. The viscous incompressible fluid flow and linear elasticity models are considered. The fluid flow and the motion of elastic body is approximated with the aid of finite element method. An attention is paid to the applied stabilization...