Related papers: Fast estimation of discretization error for FE pro…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous…
In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data…
We propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for…
This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…
This work concerns with the discontinuous Galerkin (DG)method for the time-dependent linear elasticity problem. We derive the a posteriori error bounds for semi-discrete and fully discrete problems, by making use of the stationary…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…
We present an iterative scheme, reminiscent of the Multigrid method, to solve large boundary value problems with Probabilistic Domain Decomposition (PDD). In it, increasingly accurate approximations to the solution are used as control…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
We critically assess the performance of several variants of dual and dual-primal domain decomposition strategies in problems with fixed subdomain partitioning and high heterogeneity in stiffness coefficients typically arising in topology…
In this paper, we study the "a posteriori" error estimate corresponding to the Brinkman-Darcy-Forchheimer problem. We introduce the variational formulation discretised by using the finite element method. Then, we establish an "a posteriori"…
We propose an efficient algorithm that combines overlapping domain decomposition and proper generalized decomposition (PGD) to construct surrogate models of linear elliptic parametric problems. The technique is composed of an offline and an…
We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…