Work

A virtual element method on polyhedra with curved faces

Year: 2025

Type: article

Abstract: In this paper, we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann non-homogeneous boundary conditions, and provides, for degree of accuracy [Formula: see text], optimal convergence rates. Whenever the exact solution is a polynomial of degree [Formula: see text], local spaces of degree [Formula: see text] ensure satisfaction of the patch test. The proposed method is theoretically analyzed in the two-dimensional case, whereas it is numerically validated both in two and three dimensions.

Source: Mathematical Models and Methods in Applied Sciences

DOI: 10.1142/s0218202526500090

Authors: Daniele Prada, Franco Brezzi, L. Donatella Marini

Institutions: Istituto di Matematica Applicata e Tecnologie Informatiche, Istituto Universitario di Studi Superiori di Pavia, University of Pavia

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7117322807

FWCI:

Cites: 20

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