Related papers: Two-level schemes for the advection equation
A framework of finite-velocity model based Boltzmann equation has been developed for convection-diffusion equations. These velocities are kept flexible and adjusted to control numerical diffusion. A flux difference splitting based kinetic…
In this work, we develop a class of stable and convergent numerical methods for the approximate solution of the viscoelastic Giesekus model in two space dimensions. The model couples the incompressible Navier--Stokes equations with an…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…
Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…
The field theoretic renormalization group and the operator product expansion are applied to the stochastic model of a passively advected vector field. The advecting velocity field is generated by the stochastic Navier-Stokes equation with…
We introduce a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…
In this note we study the asymptotic mean-square stability for two-step schemes applied to a scalar stochastic differential equation (sde) and applied to systems of sdes. We derive necessary and sufficient conditions for the asymptotic…
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are…
We study the long time behaviour of a dynamical system strongly linked to the anti-diffusive scheme of Despr\'es and Lagoutiere for the $1$-dimensional transport equation. This scheme is nondiffusive in the sens that discontinuities are not…
In this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Simple modifications for higher-order Godunov-type difference schemes are presented which allow for accurate advection of multi-fluid flows in hydrodynamic simulations. The constraint that the sum of all mass fractions has to be equal to…
Artificial viscosity is traditionally interpreted as a positive, spatially acting regularization introduced to stabilize numerical discretizations of hyperbolic conservation laws. In this work, we report a data-driven discovery that…
The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently there were proposed some…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
Motivated by considering partial differential equations arising from conservation laws posed on evolving surfaces, a new numerical method for an advection problem is developed and simple numerical tests are performed. The method is based on…
In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We…
Advection-diffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent…