Related papers: A Posteriori Error Analysis of Fluid-Stucture Inte…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
The Richards equation is commonly used to model the flow of water and air through soil, and it serves as a gateway equation for multiphase flows through porous media. It is a nonlinear advection-reaction-diffusion equation that exhibits…
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…
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…
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 study, we employ the variational multiscale (VMS) concept to develop a posteriori error estimates for the stationary convection-diffusion-reaction equation. The variational multiscale method is based on splitting the continuous part…
In this work we present an a posteriori error indicator for approximation schemes of Runge-Kutta-discontinuous-Galerkin type arising in applications of compressible fluid flows. The purpose of this indicator is not only for mesh adaptivity,…
We consider the frequency response problem and derive a posteriori error estimates for the discrete error in a reduced finite element model obtained using the component mode synthesis (CMS) method. We provide estimates in a linear quantity…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We…
A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect…
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…
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 work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…
This paper focuses on a posteriori error estimates for a pressure-robust finite element method, which incorporates a divergence-free reconstruction operator, within the context of the distributed optimal control problem constrained by the…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed…
We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…
A posteriori error estimates are derived in the context of two-dimensional structural elastic shape optimization under the compliance objective. It is known that the optimal shape features are microstructures that can be constructed using…
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…