We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element – finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is u...

This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to discretize in time and a HODIE compact fourth order finite difference scheme to discretize in space, which is defined on a priori special meshes condensing the grid points...

In this paper, we study finite volume element (FVE) method for convection–diffusion–reaction equations in a two-dimensional convex polygonal domain. These types of equations arise in the modeling of a waste scenario of a radioactive contaminant transport and reaction in flowing groundwater. Both spatially discrete scheme and discrete-in-time scheme are analyzed in this paper. For the spatially ...

Conditions on the stabilization parameters are explored for different approaches in deriving error estimates for the SUPG finite element stabilization of time-dependent convectiondiffusion-reaction equations. Exemplarily, it is shown for the SUPG method combined with the backward Euler scheme that standard energy arguments lead to estimates for stabilization parameters that depend on the length...

A rather general semilinear parabolic problem is studied together with its spatially semidiscrete nite element approximation. Both problems are formulated within the framework of nonlinear semigroups in the Sobolev space H 1 ((). The main result is an error estimate for solutions with initial data in H 1 ((), valid during an arbitrary nite time interval. The proof is based on the semigroup form...

Using a slightly diierent discretization scheme in time and adapting the approach in Nochetto et al: (1998) for analysing the time discretization error in the backward Euler method, we improve on the error bounds derived in (i) Barrett and Blowey (1998) and (ii) Barrett and Blowey (1999c) for a fully practical piece-wise linear nite element approximation of a model for phase separation of a mul...

We consider an initialand Dirichlet boundaryvalue problem for a fourth-order linear stochastic parabolic equation, in two or three space dimensions, forced by an additive space-time white noise. Discretizing the space-time white noise a modeling error is introduced and a regularized fourthorder linear stochastic parabolic problem is obtained. Fully-discrete approximations to the solution of the...

We develop and analyze methods based on combining the lowest-order mixed finite element method with backward Euler time discretization for the solution of diffusion problems on dynamically changing meshes. The methods developed are shown to preserve the optimal rate error estimates that are well known for static meshes. The novel aspect of the scheme is the construction of a linear approximatio...

This work concerns the mathematical modeling and computer simulations of the heat transfer process. The core is solving the time-dependent partial differential equation of parabolic type. Instead of a uniform discretization of the considered time interval, an adaptive time-stepping procedure is applied in an effort to decrease the simulation time. The procedure is based on the local comparison ...

Radio-frequency ablation is a low invasive technique for treatment of liver tumors. This work concerns the mathematical modeling and computer simulation of the heat transfer process. The core is solving the time-dependent partial differential equation of parabolic type. Instead of a uniform discretization of the considered time interval, an adaptive time-stepping procedure is applied in an effo...