Related papers: Analysis of the SDFEM in a modified streamline dif…
In this technical report, we present estimations of the discrete Green's function of the streamline diffusion finite element method (SDFEM) on Shishkin triangular meshes for problems with only exponential layers.
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…
In this paper, we describe a stable finite element formulation for advection-diffusion-reaction problems that allows for robust automatic adaptive strategies to be easily implemented. We consider locally vanishing, heterogeneous, and…
We discuss nonconforming virtual element method for convection dominated (diffusive coefficient is very small compared to convective coefficient and reac- tion coefficient ) convection-diffusion-reaction equation using L^2 projection…
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…
This paper introduces a numerical approach to solve singularly perturbed convection diffusion boundary value problems for second-order ordinary differential equations that feature a small positive parameter {\epsilon} multiplying the…
We propose the estimates of the discrete Green function for the stream- line diffusion finite element method (SDFEM) on Shishkin meshes.
In this article, a parameter-uniform numerical method is presented to solve one-dimensional singularly perturbed parabolic convection-diffusion turning point problem exhibiting two exponential boundary layers. We study the asymptotic…
A recently developed Eulerian finite element method is applied to solve advection-diffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless…
A finite difference method is constructed for a singularly perturbed convection diffusion problem posed on an annulus. The method involves combining polar coordinates, an upwind finite difference operator and a piecewise-uniform Shishkin…
We proposed a structure-preserving stabilized parametric finite element method (SPFEM) for the evolution of closed curves under anisotropic surface diffusion with an arbitrary surface energy $\hat{\gamma}(\theta)$. By introducing a…
We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…
The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced…
For convection dominated problems, the streamline upwind Petrov--Galerkin method (SUPG), also named streamline diffusion finite element method (SDFEM), ensures a stable finite element solution. Based on robust a posteriori error estimators,…
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…
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…
We propose a structure-preserving parametric finite element method (SP-PFEM) for discretizing the surface diffusion of a closed curve in two dimensions (2D) or surface in three dimensions (3D). Here the "structure-preserving" refers to…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…