6 citations · 21 across the 10 of their papers we have counts for
14 papers
Quasi-convergence of an implementation of optimal balance by backward-forward nudging
G. Tuba Masur, Haidar Mohamad, Marcel Oliver
Optimal balance is a non-asymptotic numerical method to compute a point on the slow manifold for certain two-scale dynamical systems. It works by solving a modified version of the…
Variational balance models for the three-dimensional Euler-Boussinesq equations with full Coriolis force
Gözde Özden, Marcel Oliver
We derive a semi-geostrophic variational balance model for the three-dimensional Euler--Boussinesq equations on the non-traditional -plane under the rigid lid approximation. The…
Conditional uniqueness of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit
Zymantas Darbenas, Rein van der Hout, Marcel Oliver
We study the question of uniqueness of weak solution to the fast reaction limit of the Keller and Rubinow model for Liesegang rings as introduced by Hilhorst et al. (J. Stat. Phys.…
High-order uniformly accurate time integrators for semilinear wave equations of Klein-Gordon type in the non-relativistic limit
Haidar Mohamad, Marcel Oliver
We introduce a family of high-order time semi-discretizations for semilinear wave equations of Klein--Gordon type with arbitrary smooth nonlinerities that are uniformly accurate in…
Long-time asymptotics of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit
Zymantas Darbenas, Rein van der Hout, Marcel Oliver
We consider the Keller--Rubinow model for Liesegang rings in one spatial dimension in the fast reaction limit as introduced by Hilhorst, van der Hout, Mimura, and Ohnishi in 2007.…
Breakdown of Liesegang precipitation bands in a simplified fast reaction limit of the Keller-Rubinow model
Zymantas Darbenas, Marcel Oliver
We study solutions to the integral equation \[ ω(x) = Γ- x^2 \int_{0}^1 K(θ) \, H(ω(xθ)) \, \mathrm d θ\] where , is a weakly degenerate kernel satisfying, among other pro…
Numerical integration of functions of a rapidly rotating phase
Haidar Mohamad, Marcel Oliver
We present an algorithm for the efficient numerical evaluation of integrals of the form \[ I(ω) = \int_0^1 F( x,\mathrm e^{\mathrm i ωx}; ω) \, \mathrm d x \] for sufficiently smoo…
Geometric Lagrangian averaged Euler-Boussinesq and primitive equations
Gualtiero Badin, Marcel Oliver, Sergiy Vasylkevych
In this article we derive the equations for a rotating stratified fluid governed by inviscid Euler-Boussinesq and primitive equations that account for the effects of the perturbati…
Optimal balance via adiabatic invariance of approximate slow manifolds
Georg A. Gottwald, Haidar Mohamad, Marcel Oliver
We analyze the method of optimal balance which was introduced by Viudez and Dritschel (J. Fluid Mech. 521, 2004, pp. 343-352) to provide balanced initializations for two-dimensiona…
Comparison of variational balance models for the rotating shallow water equations
David G. Dritschel, Georg A. Gottwald, Marcel Oliver
We present an extensive numerical comparison of a family of balance models appropriate to the semi-geostrophic limit of the rotating shallow water equations, and derived by variati…
Exponentially accurate Hamiltonian embeddings of symplectic A-stable Runge--Kutta methods for Hamiltonian semilinear evolution equations
Claudia Wulff, Marcel Oliver
We prove that a class of A-stable symplectic Runge--Kutta time semidiscretizations (including the Gauss--Legendre methods) applied to a class of semilinear Hamiltonian PDEs which a…
Stability under Galerkin truncation of A-stable Runge--Kutta discretizations in time
Marcel Oliver, Claudia Wulff
We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scal…
A-stable Runge-Kutta methods for semilinear evolution equations
Marcel Oliver, Claudia Wulff
We consider semilinear evolution equations for which the linear part generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert s…
The vortex blob method as a second-grade non-Newtonian fluid
Marcel Oliver, Steve Shkoller
We show that a certain class of vortex blob approximations for ideal hydrodynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-…