Related papers: A residual a posteriori error estimate for the tim…
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
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 present a numerical investigation of residual-based a posteriori error estimation for finite element discretizations of convection--diffusion equations stabilized by algebraic flux correction and related algebraic stabilization…
We devise an a posteriori error estimator for an affine optimal control problem subject to a semilinear elliptic PDE and control constraints. To approximate the problem, we consider a semidiscrete scheme based on the variational…
A posteriori upper and lower bounds are derived for the linear finite element method (FEM) for the Helmholtz equation with large wave number. It is proved rigorously that the standard residual type error estimator seriously underestimates…
The convergence of an adaptive mixed finite element method for general second order linear elliptic problems defined on simply connected bounded polygonal domains is analyzed in this paper. The main difficulties in the analysis are posed by…
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…
We propose an adaptive finite element method for the solution of a coefficient inverse problem of simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions in the Maxwell's system using limited boundary…
For elliptic interface problems in two- and three-dimensions with a possible very low regularity, this paper establishes a priori error estimates for the Raviart-Thomas and Brezzi-Douglas-Marini mixed finite element approximations. These…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
In this article, we aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsche's method for Poisson problems with Dirichlet boundary condition. The computation of the…
We introduce a new $hp$-adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy…
We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite element spaces, that are allowed to change in time. Our main…
A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the…
In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are studied for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and…
A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We…
We consider the approximation of singularly perturbed linear second-order boundary value problems by $hp$-finite element methods. In particular, we include the case where the associated differential operator may not be coercive. Within this…
We derive and discuss a posteriori error estimators for Galerkin and collocation IGA boundary element methods for weakly-singular integral equations of the first-kind in 2D. While recent own work considered the Faermann residual error…
Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such…