Related papers: Generalised gradients for virtual elements and app…
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…
We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local $H^1$ error in a interior subdomain is bounded by a term…
The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…
We derive an anisotropic a posteriori error estimate for the adaptive conforming Virtual Element approximation of a paradigmatic two-dimensional elliptic problem. In particular, we introduce a quasi-interpolant operator and exploit its…
The gradient discretisation method (GDM) is a generic framework designed recently, as a discretise in spatial space, to partial differential equations. This paper aims to use the GDM to establish a first general error estimate for numerical…
We present an equilibration-based a posteriori error estimator for N\'ed\'elec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for N\'ed\'elec elements of…
This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the…
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…
A residual-based a posteriori error estimator is proposed for the incompressible Oseen problem in the convection-dominated regime. The SUPG/PSPG/grad-div stabilized finite element method is used as discretization. The error estimator…
In this paper we propose and analyze a virtual element method for the two dimensional non-symmetric diffusion-convection eigenvalue problem in order to derive a priori and a posteriori error estimates. Under the classic assumptions of the…
In this paper we consider finite element approaches to computing the mean curvature vector and normal at the vertices of piecewise linear triangulated surfaces. In particular, we adopt a stabilization technique which allows for first order…
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on…
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…
We propose a new heuristic goal-oriented a posteriori error estimator that connects the dual weighted residual method with equilibrated a posteriori error estimation. Our numerical experiments demonstrate the practical reliability of the…
We propose Neural Gradient Learning (NGL), a deep learning approach to learn gradient vectors with consistent orientation from 3D point clouds for normal estimation. It has excellent gradient approximation properties for the underlying…
A novel residual-type {\it a posteriori} error analysis technique is developed for multipoint flux mixed finite element methods for flow in porous media in two or three space dimensions. The derived {\it a posteriori} error estimator for…
An ensemble method is introduced that utilizes randomization and loss function gradients to compute a prediction. Multiple weakly-correlated estimators approximate the gradient at randomly sampled points on the error surface and are…
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…
We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep…
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,…