Related papers: A preconditioning technique for all-at-once system…
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Gr\"unwald difference (tempered-WSGD) operators for the tempered fractional diffusion equation. We also show stability and…
We present a new method for the nonlinear approximation of the solution manifolds of parameterized nonlinear evolution problems, in particular in hyperbolic regimes with moving discontinuities. Given the action of a Lie group on the…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate that the construction of a uniformly accurate fifth-order…
The computation time for reservoir simulation is dominated by the linear solver. The sets of linear equations which arise in reservoir simulation have two distinctive features: the problems are usually highly anisotropic, with a dominant…
The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for…
The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the…
In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our…
This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to…
Mathematical models for flow and reactive transport in porous media often involve non-linear, degenerate parabolic equations. Their solutions have low regularity, and therefore lower order schemes are used for the numerical approximation.…
Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage. Modeling this problem accurately presents significant…
The present works is focused on studying bifurcating solutions in compressible fluid dynamics. On one side, the physics of the problem is thoroughly investigated using high-fidelity simulations of the compressible Navier-Stokes equations…
We propose a Fourier pseudo-spectral scheme for the space-fractional nonlinear Schr\"odinger equation. The proposed scheme has the following features: it is linearly implicit, it preserves two invariants of the equation, its unique…
Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations, but is better described by fractional diffusion models. The nonlocal nature of the fractional diffusion operators makes substantially…
The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled…
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…