9 papers
On structure-preserving and pointwise conservative continuous DG schemes for hyperbolic systems
Rémi Abgrall, Michael Dumbser, Pierre-Henri Maire +1
We present a new class of structure-preserving semi-discrete continuous-discontinuous Galerkin (CG-DG) finite element schemes for linear and nonlinear hyperbolic systems of partial…
Robust H(curl)-based finite element methods for the incompressible MHD system
Lourenço Beirão da Veiga, Sergio Gómez, Ilaria Perugia +1
We propose and analyze a class of finite element methods for the time-dependent incompressible magnetohydrodynamics system based on -conforming discretizations fo…
H(curl)-based approximation of the Stokes problem with slip boundary conditions
Wietse M. Boon, Ralf Hiptmair, Wouter Tonnon +1
Reformulating the incompressible Stokes equations with the velocity sought in H(curl) has recently emerged as a promising approach for the design of helicity-preserving schemes in…
Stability, convergence, and geometric properties of second-order-in-time space-time discretizations for linear and semilinear wave equations
Matteo Ferrari, Ilaria Perugia, Enrico Zampa
We revisit second-order-in-time space-time discretizations of the linear and semilinear wave equations by establishing precise equivalences with first-order-in-time formulations. F…
Finite element exterior calculus for time-dependent Hamiltonian partial differential equations
Ari Stern, Enrico Zampa
The success of symplectic integrators for Hamiltonian ODEs has led to a decades-long program of research seeking analogously structure-preserving numerical methods for Hamiltonian…
H(curl)-based approximation of the Stokes problem with weakly enforced no-slip boundary conditions
Wietse M. Boon, Wouter Tonnon, Enrico Zampa
In this work, we show how to impose no-slip boundary conditions for an H(curl)-based formulation for incompressible Stokes flow, which is used in structure-preserving discretizatio…