Related papers: A short perspective on a posteriori error control …
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,…
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…
The a posteriori analysis of the discretization error and the modeling error is studied for a compliance cost functional in the context of the optimization of composite elastic materials and a two-scale linearized elasticity model. A…
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a…
This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
This work deals with the a posteriori error estimates for the Darcy-Forchheimer problem. We introduce the corresponding variational formulation and discretize it by using the finite-element method. A posteriori error estimate with two types…
Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described…
In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and…
In a previous work, we introduced a discretization scheme for a constrained optimal control problem involving the fractional Laplacian. For such a control problem, we derived optimal a priori error estimates that demand the convexity of the…
A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…
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…
The most critical component of any adaptive numerical quadrature routine is the estimation of the integration error. Since the publication of the first algorithms in the 1960s, many error estimation schemes have been presented, evaluated…
An explicit and computable error estimator for the $hp$ version of the virtual element method (VEM), together with lower and upper bounds with respect to the exact energy error, is presented. Such error estimator is employed to provide $hp$…
Nowadays, a posteriori error control methods have formed a new important part of the numerical analysis. Their purpose is to obtain computable error estimates in various norms and error indicators that show distributions of global and local…
We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…
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…
We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…
Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality…
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…