English
Related papers

Related papers: Bulk-surface virtual element method for systems of…

200 papers

The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The…

Numerical Analysis · Mathematics 2014-03-04 Joerg Grande , Maxim Olshanskii , Arnold Reusken

The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…

Numerical Analysis · Mathematics 2024-08-21 Timo Heister , Maxim A. Olshanskii , Vladimir Yushutin

The Virtual Element Method (VEM) is a well-established framework for solving partial differential equations on polygonal and polyhedral meshes. In this paper, we introduce a novel hybrid VEM that integrates both conforming and nonconforming…

Numerical Analysis · Mathematics 2026-05-28 L. Beirão da Veiga , F. Dassi , A. Russo , M. Trezzi

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…

Numerical Analysis · Mathematics 2023-10-31 Hauke Gravenkamp , Albert A. Saputra , Sascha Eisenträger

The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…

Numerical Analysis · Mathematics 2018-10-24 Edoardo Artioli , Lourenco Beirao da Veiga , Carlo Lovadina , Elio Sacco

We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…

Numerical Analysis · Mathematics 2021-05-07 Elena Bachini , Gianmarco Manzini , Mario Putti

The scaled boundary finite element method (SBFEM) is a semi-analytical computational scheme, which is based on the characteristics of the finite element method (FEM) and combines the advantages of the boundary element method (BEM). This…

Numerical Analysis · Mathematics 2024-10-22 Yang Yang , Zongliang Zhang , Yelin Feng

The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…

Numerical Analysis · Mathematics 2023-07-19 Alexey Y. Chernyshenko , Maxim A. Olshanskii

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element…

Numerical Analysis · Mathematics 2021-12-28 Gianmarco Manzini , Annamaria Mazzia

The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…

Numerical Analysis · Mathematics 2025-10-03 Ramsharan Rangarajan , N. Sukumar

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…

Numerical Analysis · Mathematics 2021-03-23 Fleurianne Bertrand , Daniele Boffi , Gonzalo G. de Diego

The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…

Numerical Analysis · Mathematics 2023-10-06 L. L. Yaw

The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis…

Mathematical Software · Computer Science 2021-04-21 Shukai Ya , Sascha Eisenträger , Chongmin Song , Jianbo Li

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…

Numerical Analysis · Mathematics 2016-12-28 Paola F. Antonietti , Matteo Bruggi , Simone Scacchi , Marco Verani

This paper presents an initial exploration of stress-assisted diffusion problems in three dimensions within the framework of the virtual element method (VEM). Hilbert spaces enriched with parameter-weighted norms, the extended…

Numerical Analysis · Mathematics 2025-02-05 Andres E. Rubiano

This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…

Numerical Analysis · Mathematics 2021-10-28 Toru Takahashi , Tetsuro Hirai , Hiroshi Isakari , Toshiro Matsumoto

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. We adopt the Hellinger--Reissner variational principle to construct a weak equilibrium…

Numerical Analysis · Mathematics 2024-02-29 Alvin Chen , Joseph E. Bishop , N. Sukumar

The third medium contact has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, the third medium contact introduces a third medium between two…

Numerical Analysis · Mathematics 2025-09-05 Bing-Bing Xu , Peter Wriggers

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…

Numerical Analysis · Mathematics 2016-05-25 Peter Hansbo , Mats G. Larson , Sara Zahedi

We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…

Numerical Analysis · Mathematics 2023-07-19 L. Beirão da Veiga , C. Lovadina , D. Mora