We present a fully-coupled monolithic formulation of the fluid-structure interaction of an
incompressible fluid on a moving domain with a nonlinear hyperelastic solid. The arbitrary …

The objective of this article is to give an overview of finite element methods that currently are
used extensively in academia and industry. The method is described in general terms, the …

We propose a discretization‐free approach based on the physics‐informed neural network
(PINN) method for solving the coupled advection‐dispersion equation (ADE) and Darcy flow …

The present article reviews the variational multiscale method as a framework for the
development of computational methods for the simulation of laminar and turbulent flows …

Numerous studies have suggested that medical image derived computational mechanics
models could be developed to reduce mortality and morbidity due to cardiovascular …

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and
SimulatiON) software environment. CRIMSON provides a powerful, customizable and user …

In this paper we analyze a stabilized finite element approximation for the incompressible
Navier–Stokes equations based on the subgrid-scale concept. The essential point is that we …

The variational multiscale method is reviewed as a framework for developing computational
methods for large-eddy simulation of turbulent flow. In contrast to other articles reviewing this …

We develop divergence-conforming B-spline discretizations for the numerical solution of the
steady Navier–Stokes equations. These discretizations are motivated by the recent theory of …

We propose a new model-based unsupervised learning method, called VarNet, for the
solution of partial differential equations (PDEs) using deep neural networks. Particularly, we …