Related papers: Two-level schemes for the advection equation
In part I we considered the problem of convergence to a saddle point of a concave-convex function via gradient dynamics and an exact characterization was given to their asymptotic behaviour. In part II we consider a general class of…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
We prove in this paper the weak consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over the cells of the mesh and over the time steps. It yields an extension of…
Stochastic MPECs have found increasing relevance for modeling a broad range of settings in engineering and statistics. Yet, there seem to be no efficient first/zeroth-order schemes equipped with non-asymptotic rate guarantees for resolving…
We consider stability of regimes of hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries, to perturbations involving large spatial and temporal scales. Equations governing the…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…
The Convected Scheme (CS) is a `forward-trajectory' semi-Lagrangian method for solution of transport equations, which has been most often applied to the kinetic description of plasmas and rarefied neutral gases. In its simplest form, the CS…
It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
Fundamental solution of a space fractional convection equation of order $\alpha$ is the probability density function of L\'{e}vy flights with long-tailed $\alpha$-stable jump length distribution. By studying an upwind second-order implicit…
Schemes with the second-order approximation in time are considered for numerical solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator. The implicit two-level scheme based on the Pad\'{e}…
This paper studies the stability properties of a two dimensional relative velocity scheme for the Navier-Stokes equations. This scheme inspired by the cascaded scheme has the particularity to relax in a frame moving with a velocity field…
We study the stability of a two-dimensional Lax-Wendroff scheme in a quarter-plane. Following our previous work, we aim here at adapting the energy method in order to study second order extrapolation boundary conditions. We first show on…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
This work deals with a number of questions relative to the discrete and continuous adjoint fields associated with the compressible Euler equations and classical aerodynamic functions. The consistency of the discrete adjoint equations with…