Related papers: Adaptive quadratic finite element method for the u…
Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory…
Recently proposed formulation of the Boundary Element Method for adhesive contacts has been generalized for contacts of functionally graded materials with and without adhesion. First, proceeding from the fundamental solution for single…
The convection-diffusion eigenvalue problems are hot topics, and computational mathematics community and physics community are concerned about them in recent years. In this paper, we consider the a posteriori error analysis and the adaptive…
We derive a residual-based a posteriori error estimator for the conforming hp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is…
This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov-Maxwell system. The SD scheme yields a weak formulation, that corresponds to an…
In this paper, we propose a \( C^0 \)-conforming finite element method for the Chafee-Infante equation with a finite-parameter feedback control. We establish error analysis for both the state variable and the control variable for the…
This paper introduces a novel a posteriori error estimation framework for the enriched Galerkin (EG) finite element method applied to linear parabolic equations. While the EG method has been recognized for its local conservation property…
An element based adaptation method is developed for an anisotropic a posteriori error estimator. The adaptation does not make use of a metric, but instead equidistributes the error over elements using local mesh modifications. Numerical…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
This paper proposes and analyzes an a posteriori error estimator for the finite element multi-scale discretization approximation of the Steklov eigenvalue problem. Based on the a posteriori error estimates, an adaptive algorithm of shifted…
We propose a posteriori error estimators for classical low-order inf-sup stable and stabilized finite element approximations of the Stokes problem with singular sources in two and three dimensional Lipschitz, but not necessarily convex,…
The primal-dual gap is a natural upper bound for the energy error and, for uniformly convex minimization problems, also for the error in the energy norm. This feature can be used to construct reliable primal-dual gap error estimators for…
In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
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 energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrary space dimension. Using an equilibrated flux…
The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous piecewise linear pressure elements is known to constitute a…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
We derive a posteriori error estimates in the $L_\infty((0,T];L_\infty(\Omega))$ norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction technique introduced by Makridakis and Nochetto and heat…
In this work, we derive a $\gamma$-robust a posteriori error estimator for finite element approximations of the Allen-Cahn equation with variable non-degenerate mobility. The estimator utilizes spectral estimates for the linearized steady…