About estimates for the spatially homogeneous Boltzmann equation
About porosity parameters with the application of general similarity method to the case of a dissociated gas flow in the boundary layer
About steady transport equation I – -approach in domains with smooth boundaries
We investigate the steady transport equation in various domains (bounded or unbounded) with smooth noncompact boundaries. The functions are supposed to be small in appropriate norms. The solution is studied in spaces of Sobolev type (classical Sobolev spaces, Sobolev spaces with weights, homogeneous Sobolev spaces, dual spaces to Sobolev spaces). The particular stress is put onto the problem to extend the results to as less regular vector fields , as possible (conserving the requirement of...
About steady transport equation. II: Schauder estimates in domains with smooth boundaries.
About the decay of surface waves on viscous fluids without surface tension
We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.
About the interface of some nonlinear diffusion problems.
About the Resolvent of an Operator from Fluid Dynamics.
Abrupt and smooth separation of free boundaries in flow problems
Abstracts of theses in mathematics
Žemlička, Jan: Structure of steady rings. Zemek, Martin: On some aspects of subdifferentiality of functions on Banach spaces. Hlubinka, Daniel: Construction of Markov kernels with application for moment problem solution. Somberg, Petr: Properties of the BGG resolution on the spheres. Krump, Lukáš: Construction of Bernstein-Gelfand-Gelfand for almost hermitian symmetric structures. Kolář, Jan: Simultaneous extension operators. Porosity.
Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions
In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure....
Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions
In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of...
Acceleration of two-grid stabilized mixed finite element method for the Stokes eigenvalue problem
This paper provides an accelerated two-grid stabilized mixed finite element scheme for the Stokes eigenvalue problem based on the pressure projection. With the scheme, the solution of the Stokes eigenvalue problem on a fine grid is reduced to the solution of the Stokes eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. By solving a slightly different linear problem on the fine grid, the new algorithm significantly improves the theoretical error...
Acceleration waves in thermo-viscous fluids
Accurate and online-efficient evaluation of the a posteriori error bound in the reduced basis method
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive...
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere. III: For arbitrary Prandtl number.
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere. I: For large Prandtl number.
Acoustic-gravity waves in a viscous and thermally conducting isothermal atmosphere. II: For small Prandtl number.
Acoustics of a stratified poroelastic composite.