Related papers: A convection-diffusion problem with a small variab…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…
The linear singularly perturbed convection-diffusion problem in one dimension is considered and its discretization on a Bakhvalov-type mesh is analyzed. The preconditioning technique is used to obtain the pointwise convergence uniform in…
This work addresses techniques to solve convection-diffusion problems based on Hermite interpolation. We extend to the case of these equations a Hermite finite element method providing flux continuity across inter-element boundaries, shown…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
In this article, we address singularly perturbed two-parameter parabolic problem of the reaction-convection-diffusion type in two dimensions. These problems exhibit discontinuities in the source term and convection coefficient at particular…
A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The…
Convection-diffusion of heat transfer is one of the important phenomena in fluid flow and industrial problems. The involved parameters, boundary conditions, and material properties are greatly affecting the same. As such, the uncertainness…
In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…
Convection-diffusion-reaction equations model the conservation of scalar quantities. From the analytic point of view, solution of these equations satisfy under certain conditions maximum principles, which represent physical bounds of the…
We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution…
In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a…
This paper studies adaptive least-squares finite element methods for convection-dominated diffusion-reaction problems. The least-squares methods are based on the first-order system of the primal and dual variables with various ways of…
Error estimates of finite element methods for reaction-diffusion Problems are often realized in the related energy norm. In the singularly perturbed case, however, this norm is not adequate. A different scaling of the $H^1$ seminorm leads…
A singularly perturbed convection-diffusion problem posed on the unit square in $\mathbb{R}^2$, whose solution has exponential boundary layers, is solved numerically using the local discontinuous Galerkin (LDG) method with piecewise…
In this paper, we consider control constrained $L^2-$Dirichlet boundary control of a convection-diffusion equation on a two dimensional convex polygonal domain. We discretize the control problem based on the local discontinuous Galerkin…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
We develop an ultra-weak variational formulation of a fractional advection diffusion problem in one space dimension and prove its well-posedness. Based on this formulation, we define a DPG approximation with optimal test functions and show…
This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities…
We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…