Related papers: Sharper error estimates for Virtual Elements and a…
In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime (r > 2) including both…
A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer.…
Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such…
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
In this paper we introduce and analyze the residual-based a posteriori error estimation of the partially penalized immersed finite element method for solving elliptic interface problems. The immersed finite element method can be naturally…
The Discrete Element Method is widely employed for simulating granular flows, but conventional integration techniques may produce unphysical results for simulations with static friction when particle size ratios exceed $R \approx 3$. These…
The aim of this paper is twofold. On the one hand, we test numerically the performance of mixed virtual elements in three dimensions for the first time in the literature to solve the mixed formulation of three-dimensional elliptic equations…
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solution of very large linear systems arising from elliptic…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of…
We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a…
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…
A virtual element method (VEM) with the first order optimal convergence order is developed for solving two-dimensional Maxwell interface problems on a special class of polygonal meshes that are cut by the interface from a background…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
In this paper, we analyze a virtual element method (VEM) for solving a non-selfadjoint fourth-order eigenvalue problem derived from the transmission eigenvalue problem. We write a variational formulation and propose a $C^1$-conforming…