Related papers: Simplex-averaged finite element methods for $H({\r…
We extend the applicability of the popular interior-penalty discontinuous Galerkin (dG) method discretizing advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In…
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,…
An initial-boundary value problem for the time-fractional diffusion equation is discretized in space using continuous piecewise-linear finite elements on a polygonal domain with a re-entrant corner. Known error bounds for the case of a…
This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…
We consider a semi-discrete finite element approximation for a system consisting of the evolution of a planar curve evolving by forced curve shortening flow inside a given bounded domain $\Omega \subset \mathbb{R}^2$, such that the curve…
We consider a singularly perturbed convection-diffusion with exponential and characteristic boundary layers. The problem is numerically solved by the FEM and SDFEM method with bilinear elements on a graded mesh. For the FEM we prove almost…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…
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 discuss the 2D convection-diffusion-reaction equation with variable smooth coefficients and the Dirichlet boundary condition on a complicated, thin, and curved domain. We propose the fourth-order compact FDM at every grid…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in…
In [24], we proposed H(curl^2)-conforming elements on both a triangle and a rectangle. This family of elements provides a brand new method to solve the quad-curl problem in 2 dimensions. In this paper, we turn our focus to 3 dimensions and…
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order…
In this paper we present and analyze a constraint energy minimizing generalized multiscale finite element method for convection diffusion equation. To define the multiscale basis functions, we first build an auxiliary multiscale space by…
This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…