相关论文: A posteriori error estimates for sequential lamina…
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…
A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems of Dirichlet and mixed boundary conditions are proposed. Stability and efficiency of the estimators are proved. Finally, we provide…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
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…
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,…
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 finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use $H^1$-conforming…
Multilevel methods represent a powerful approach in numerical solution of partial differential equations. The multilevel structure can also be used to construct estimates for total and algebraic errors of computed approximations. This paper…
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…
In this work, we further develop multigoal-oriented a posteriori error estimation with two objectives in mind. First, we formulate goal-oriented mesh adaptivity for multiple functionals of interest for nonlinear problems in which both the…
Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…
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…
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 combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived generalized Marini formula. The a posteriori error estimates are…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
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 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…
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…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…