Related papers: Numerical analysis for time-dependent advection-di…
In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We establish stable finite element (FE) approximations of convection-diffusion initial boundary value problems using the automatic variationally stable finite element (AVS-FE) method. The transient convection-diffusion problem leads to…
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular perturbed case when the convection term dominates the…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in $\Bbb{R}^d$ defines a $d$-dimensional space-time manifold in the space-time continuum…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
Analysis of an interface stabilised finite element method for the scalar advection-diffusion-reaction equation is presented. The method inherits attractive properties of both continuous and discontinuous Galerkin methods, namely the same…
Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. Two important points that we make are: nonsmooth initial data…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
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…
This paper analyzes a time-stepping discontinuous Galerkin method for fractional diffusion-wave problems. This method uses piecewise constant functions in the temporal discretization and continuous piecewise linear functions in the spatial…
We extend the discontinuous Galerkin (DG) framework to the analysis of first-order hyperbolic and advection-dominated problems posed on implicitly defined surfaces. The focus will be on the hyperbolic part, which is discretised using a…
We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The residual-based error estimator is proven to be reliable and…