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- Michael M. J. Proot, Marc I. Gerritsma
- J. Sci. Comput.
- 2002

- Michael M. J. Proot, Marc I. Gerritsma
- J. Sci. Comput.
- 2006

- Michael M. J. Proot, Marc I. Gerritsma
- Numerical Algorithms
- 2005

In this paper the extension of the Legendre least-squares spectral element formulation to Chebyshev polynomials will be explained. The new method will be applied to the incompressible Navier-Stokes equations and numerical results, obtained for the lid-driven cavity flow at Reynolds numbers varying between 1000 and 7500, will be compared with the commonly… (More)

- Bart De Maerschalck, Marc I. Gerritsma
- Numerical Algorithms
- 2005

Chebyshev polynomials of the first kind are employed in a space-time least-squares spectral element formulation applied to linear and nonlinear hyperbolic scalar equations. No stabilization techniques are required to render a stable, high order accurate scheme. In parts of the domain where the underlying exact solution is smooth, the scheme exhibits… (More)

- Marc I. Gerritsma, Jan-Bart van der Steen, Peter Vos, George E. Karniadakis
- J. Comput. Physics
- 2010

Article history: Received 11 May 2009 Received in revised form 11 June 2010 Accepted 21 July 2010 Available online 13 August 2010

- Marc I. Gerritsma, Tim N. Phillips
- SIAM J. Scientific Computing
- 1999

- Artur Palha, Marc I. Gerritsma
- LSSC
- 2009

- Jasper J. Kreeft, Marc I. Gerritsma
- ArXiv
- 2012

This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretization method relies on the construction of a conforming discrete Hodge decomposition, that is based on a bounded projection operator that commutes with the exterior derivative. The… (More)

- Jasper J. Kreeft, Marc I. Gerritsma
- J. Comput. Physics
- 2013

In this paper we apply the recently developed mimetic discretization method [44] to the mixed formulation of the Stokes problem in terms of the vorticity-velocity-pressure formulation. The mimetic discretization presented in this paper and in [44] is a higher-order method for curvilinear quadrilaterals. It relies on the language of differential k-forms,… (More)

- Pavel B. Bochev, Marc I. Gerritsma
- Computers & Mathematics with Applications
- 2014

We use this system to motivate a new least-squares functional involving all four fields and show that its minimizer satisfies the differential equations exactly. Discretization of the four-field least-squares functional by spectral spaces compatible with the differential operators leads to a least-squares method in which the differential equations are also… (More)