Related papers: Adaptive Finite Elements with Algebraic Stabilizat…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
We review some recent advances in the field of element-based algebraic stabilization for continuous finite element discretizations of nonlinear hyperbolic problems. The main focus is on multidimensional convex limiting techniques designed…
The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…
In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes [Jha20.CAMWA] to the newly proposed algebraic stabilization schemes…
We consider finite element discretizations of Maxwell's equations coupled with a non-local hydrodynamic Drude model that accurately accounts for electron motions in metallic nanostructures. Specifically, we focus on a posteriori error…
This paper is concerned with adaptive mesh refinement strategies for the spatial discretization of parabolic problems with dynamic boundary conditions. This includes the characterization of inf-sup stable discretization schemes for a…
In this work, we propose a residual-based a posteriori error estimator for algebraic flux-corrected (AFC) schemes for stationary convection-diffusion equations. A global upper bound is derived for the error in the energy norm for a general…
The efficient and reliable approximation of convection-dominated problems continues to remain a challenging task. To overcome the difficulties associated with the discretization of convection-dominated equations, stabilization techniques…
We design and analyze a new adaptive stabilized finite element method. We construct a discrete approximation of the solution in a continuous trial space by minimizing the residual measured in a dual norm of a discontinuous test space that…
There is a wide range of stabilized finite element methods for stationary and non-stationary convection-diffusion equations such as streamline diffusion methods, local projection schemes, subgrid-scale techniques, and continuous interior…
Algebraically stabilized finite element discretizations of scalar steady-state convection-diffusion-reaction equations often provide accurate approximate solutions satisfying the discrete maximum principle (DMP). However, it was observed…
We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-dependent advection equation, we prove global-in-time existence…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
We consider an interface problem often arising in transport problems: a coupled system of partial differential equations with one (elliptic) transport equation on a bounded domain and one equation (in this case the Laplace problem) on the…
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions…
We consider second-order PDE problems set in unbounded domains and discretized by Lagrange finite elements on a finite mesh, thus introducing an artificial boundary in the discretization. Specifically, we consider the reaction diffusion…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
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…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…