
A monolithic fluidporous structure interaction finite element method
The paper introduces a fully discrete quasiLagrangian finite element me...
read it

Variational Structures in Cochain Projection Based Variational Discretizations of Lagrangian PDEs
Compatible discretizations, such as finite element exterior calculus, pr...
read it

Reduced Order Models for the QuasiGeostrophic Equations: A Brief Survey
Reduced order models (ROMs) are computational models whose dimension is ...
read it

A variational interpretation of Restricted Additive Schwarz with impedance transmission condition for the Helmholtz problem
In this paper we revisit the Restricted Additive Schwarz method for solv...
read it

A Mixed Finite Element Approximation for Fluid Flows of Mixed Regimes in Porous Media
In this paper, we consider the complex flows when all three regimes pre...
read it

A scalable variational inequality approach for flow through porous media models with pressuredependent viscosity
Mathematical models for flow through porous media typically enjoy the so...
read it

A fieldsplit preconditioning technique for fluidstructure interaction problems with applications in biomechanics
We present a novel preconditioning technique for Krylov subspace algorit...
read it
A Variational Finite Element Discretization of Compressible Flow
We present a finite element variational integrator for compressible flows. The numerical scheme is derived by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups and the associated variational principles. Given a triangulation on the fluid domain, the discrete group of diffeomorphisms is defined as a certain subgroup of the group of linear isomorphisms of a finite element space of functions. In this setting, discrete vector fields correspond to a certain subspace of the Lie algebra of this group. This subspace is shown to be isomorphic to a RaviartThomas finite element space. The resulting finite element discretization corresponds to a weak form of the compressible fluid equation that doesn't seem to have been used in the finite element literature. It extends previous work done on incompressible flows and at the lowest order on compressible flows. We illustrate the conservation properties of the scheme with some numerical simulations.
READ FULL TEXT
Comments
There are no comments yet.