Related papers: On arbitrarily regular conforming virtual element …
Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…
This paper is concerned with the analysis of a new stable space-time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on…
This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…
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…
The lowest-order Neural Approximated Virtual Element Method on polygonal elements is proposed here. This method employs a neural network to locally approximate the Virtual Element basis functions, thereby eliminating issues concerning…
We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we…
In this paper we analyze a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. We consider the classic velocity-pressure formulation which allows us to…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
In this paper, we couple regularization techniques with the adaptive $hp$-version of the boundary element method ($hp$-BEM) for the efficient numerical solution of linear elastic problems with nonmonotone contact boundary conditions. As a…
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,…
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
We extend the basic idea of Serendipity Virtual Elements from the previous case (by the same authors) of nodal ($H^1$-conforming) elements, to a more general framework. Then we apply the general strategy to the case of $H(div)$ and…
We introduce a novel residual-based a posteriori error estimator for the conforming $C^1$ Virtual Element Method (VEM) applied to the buckling eigenvalue problem, incorporating nonlinear plane stress effects in both two and three…
We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…
We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the $\boldsymbol{H}(\operatorname{grad-div})$-conforming virtual element…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…