Eighty years of the finite element method: Birth, evolution, and future

WK Liu, S Li, HS Park - Archives of Computational Methods in …, 2022 - Springer
This document presents comprehensive historical accounts on the developments of finite
element methods (FEM) since 1941, with a specific emphasis on developments related to …

A comprehensive review of educational articles on structural and multidisciplinary optimization

C Wang, Z Zhao, M Zhou, O Sigmund… - Structural and …, 2021 - Springer
Ever since the publication of the 99-line topology optimization MATLAB code (top99) by
Sigmund in 2001, educational articles have emerged as a popular category of contributions …

[LIVRE][B] An introduction to reservoir simulation using MATLAB/GNU Octave: User guide for the MATLAB Reservoir Simulation Toolbox (MRST)

KA Lie - 2019 - books.google.com
This book provides a self-contained introduction to the simulation of flow and transport in
porous media, written by a developer of numerical methods. The reader will learn how to …

Can physics-informed neural networks beat the finite element method?

TG Grossmann, UJ Komorowska, J Latz… - IMA Journal of …, 2024 - academic.oup.com
Partial differential equations play a fundamental role in the mathematical modelling of many
processes and systems in physical, biological and other sciences. To simulate such …

Construction of arbitrary order finite element degree-of-freedom maps on polygonal and polyhedral cell meshes

MW Scroggs, JS Dokken, CN Richardson… - ACM Transactions on …, 2022 - dl.acm.org
We develop a method for generating degree-of-freedom maps for arbitrary order Ciarlet-type
finite element spaces for any cell shape. The approach is based on the composition of …

[LIVRE][B] Finite elements II

A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

[LIVRE][B] Mixed finite element methods and applications

D Boffi, F Brezzi, M Fortin - 2013 - Springer
About 10 years ago, Mixed and Hybrid Finite Element Methods by F. Brezzi and M. Fortin
went out of print and we were asked to allow a second printing. The world had evolved and …

The hitchhiker's guide to the virtual element method

L Beirão da Veiga, F Brezzi, LD Marini… - … models and methods in …, 2014 - World Scientific
The Hitchhiker's Guide to the Virtual Element Method | Mathematical Models and Methods in
Applied Sciences World Scientific Search This Journal Anywhere Quick Search in Journals …

The hybrid high-order method for polytopal meshes

DA Di Pietro, J Droniou - Number 19 in Modeling, Simulation and …, 2020 - Springer
Originally introduced in [146, 158], Hybrid High-Order (HHO) methods provide a framework
for the discretisation of models based on Partial Differential Equations (PDEs) with features …

[HTML][HTML] Equivalent projectors for virtual element methods

B Ahmad, A Alsaedi, F Brezzi, LD Marini… - Computers & Mathematics …, 2013 - Elsevier
In the original virtual element space with degree of accuracy k, projector operators in the H 1-
seminorm onto polynomials of degree≤ k can be easily computed. On the other hand …