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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

We prove the convergence of an adaptive mixed finite element method (AMFEM) for (nonsymmetric) convection-diffusion-reaction equations. The convergence result holds from the cases where convection or reaction is not present to convection-or…

Numerical Analysis · Mathematics 2015-03-26 Shaohong Du , Xiaoping Xie

We study the gradient superconvergence of bilinear finite volume element (FVE) solving the elliptic problems. First, a superclose weak estimate is established for the bilinear form of the FVE method. Then, we prove that the gradient…

Numerical Analysis · Mathematics 2015-06-23 Tie Zhang , Lixin Tang

This work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on the mesh faces…

Numerical Analysis · Mathematics 2019-08-16 Ruben Sevilla , Matteo Giacomini , Antonio Huerta

In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…

Numerical Analysis · Mathematics 2022-11-07 Massimo Frittelli , Anotida Madzvamuse , Ivonne Sgura

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…

Numerical Analysis · Mathematics 2026-01-14 Yanpeng Gong , Sishuai Li , Yue Mei , Bingbing Xu , Fei Qin , Xiaoying Zhuang , Timon Rabczuk

The realization of a standard Adaptive Finite Element Method (AFEM) preserves the mesh conformity by performing a completion step in the refinement loop: in addition to elements marked for refinement due to their contribution to the global…

Numerical Analysis · Mathematics 2024-02-15 Claudio Canuto , Davide Fassino

We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the…

Numerical Analysis · Mathematics 2014-05-19 B. Ayuso de Dios , K. Lipnikov , G. Manzini

In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics,…

Computational Engineering, Finance, and Science · Computer Science 2021-10-05 Marco Lo Cascio

A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…

Numerical Analysis · Computer Science 2017-06-06 T. P. Fries

Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…

Numerical Analysis · Mathematics 2023-10-03 Alan F. Hegarty , Eugene O'Riordan

In this paper we show that bending a finite volume hyperbolic $d$-manifold $M$ along a totally geodesic hypersurface $\Sigma$ results in a properly convex projective structure on $M$ with finite volume. We also discuss various geometric…

Geometric Topology · Mathematics 2020-04-10 Samuel A. Ballas , Ludovic Marquis

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

This paper is devoted to analyze of nonconforming finite volume methods (FVMs), whose trial spaces are chosen as the nonconforming finite element (FE) spaces, for solving the second order elliptic boundary value problems. We formulate the…

Numerical Analysis · Mathematics 2016-10-31 Yuanyuan Zhang , Zhongying Chen

Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…

Computational Engineering, Finance, and Science · Computer Science 2025-11-18 Suhaib Ardah , Francisco J. Profito , Daniele Dini

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

We present a new divergence-free and well-balanced hybrid FV/FE scheme for the incompressible viscous and resistive MHD equations on unstructured mixed-element meshes in 2 and 3 space dimensions. The equations are split into subsystems. The…

Numerical Analysis · Mathematics 2025-01-29 F. Fambri , E. Zampa , S. Busto , L. Río-Martín , F. Hindenlang , E. Sonnendrücker , M. Dumbser

This paper presents two approaches: the virtual element method (VEM) and the stabilization-free virtual element method (SFVEM) for analyzing thermomechanical behavior in electronic packaging structures with geometric multi-scale features.…

Numerical Analysis · Mathematics 2025-12-29 Yanpeng Gong , Sishuai Li , Fei Qin , Bingbing Xu

Numerical computation of harmonic forms (typically called harmonic fields in three space dimensions) arises in various areas, including computer graphics and computational electromagnetics. The finite element exterior calculus framework…

Numerical Analysis · Mathematics 2016-06-24 Alan Demlow

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to…

Numerical Analysis · Mathematics 2024-06-19 Jerome Droniou , Gianmarco Manzini , Liam Yemm