Related papers: A Posteriori Error Estimates with Boundary Correct…
A posteriori error estimator is derived for an elliptic interface problem in the fictitious domain formulation with distributed Lagrange multiplier considering a discontinuous Lagrange multiplier finite element space. A posteriori error…
In this paper we develop a $C^0$-conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error analysis for this problem and derive a residual based error…
A posteriori estimates give bounds on the error between the unknown solution of a partial differential equation and its numerical approximation. We present here the methodology based on H1-conforming potential and H(div)-conforming…
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…
This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and…
In this paper, a residual-type a posteriori error estimator is proposed and analyzed for a modified weak Galerkin finite element method solving linear elasticity problems. The estimator is proven to be both reliable and efficient because it…
We consider a linear elliptic partial differential equation (PDE) with a generic uniformly bounded parametric coefficient. The solution to this PDE problem is approximated in the framework of stochastic Galerkin finite element methods. We…
In this work, we analyze the residual-based a posteriori error estimation of the multi-scale cancer invasion model, which is a system of three non-stationary reaction-diffusion equations. We present the numerical results of a study on a…
This paper considers the finite element solution of the boundary value problem of Poisson's equation and proposes a guaranteed em a posteriori local error estimation based on the hypercircle method. Compared to the existing literature on…
We present a framework that relates preconditioning with a posteriori error estimates in finite element methods. In particular, we use standard tools in subspace correction methods to obtain reliable and efficient error estimators. As a…
In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal…
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 examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques…
We design an adaptive unfitted finite element method on the Cartesian mesh with hanging nodes. We derive an hp-reliable and efficient residual type a posteriori error estimate on K-meshes. A key ingredient is a novel hp-domain inverse…
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind…
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…
The Finite Element Method (FEM) is a well-established procedure for computing approximate solutions to deterministic engineering problems described by partial differential equations. FEM produces discrete approximations of the solution with…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its…
For the finite element solution of Poisson's equation, a local a posteriori error estimation based on the Hypercircle method is proposed. Even for the solution of Poisson's equation without the $H^2$ regularity, this method can provide…