Related papers: A posteriori error analysis for a boundary element…
In this paper we analyze Nitsche's method for the stationary Boussinesq system with Navier's slip and a nonlinear boundary condition. Our analysis of the formulation establishes the robustness of a finite elements scheme in arbitrarily…
This paper introduces an explicit residual-based a posteriori error analysis for the symmetric mixed finite element method in linear elasticity after Arnold-Winther with pointwise symmetric and H(div)-conforming stress approximation.…
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…
In our work, we consider the classical density-based approach to topology optimization. We propose the modification of the discretized cost/objective functional using a posteriori error estimator for the finite element method. It can be…
We propose and analyse residual-based a posteriori error estimates for the virtual element discretisation applied to the thin plate vibration problem in both two and three dimensions. Our approach involves a conforming $C^1$ discrete…
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…
We analyse a posteriori error estimates for the discretization with mixed finite elements on simplicial or Cartesian meshes of the multigroup neutron simplified transport (SPN ) equations, in the case where a Robin (or Fourier type)…
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…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically,…
A posteriori residual and hierarchical upper bounds for the error estimates were proved when solving the hypersingular integral equation on the unit sphere by using the Galerkin method with spherical splines. Based on these a posteriori…
Based on neural network and adaptive subspace approximation method, we propose a new machine learning method for solving partial differential equations. The neural network is adopted to build the basis of the finite dimensional subspace.…
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…
This paper derives a posteriori error estimates for the mixed numerical approximation of the Laplace eigenvalue problem with homogeneous Dirichlet boundary conditions. In particular, the resulting error estimator constitutes an upper bound…
We consider a mixed variational formulation recently proposed for the coupling of the Brinkman--Forchheimer and Darcy equations and develop the first reliable and efficient residual-based a posteriori error estimator for the 2D version of…
The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is…
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 this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…
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…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…