Mimetic finite difference method

K Lipnikov, G Manzini, M Shashkov - Journal of Computational Physics, 2014‏ - Elsevier
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …

[ספר][B] Mimetic discretization methods

JE Castillo, GF Miranda - 2013‏ - books.google.com
To help solve physical and engineering problems, mimetic or compatible algebraic
discretization methods employ discrete constructs to mimic the continuous identities and …

A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier–Stokes equations

A Palha, M Gerritsma - Journal of Computational Physics, 2017‏ - Elsevier
In this work we present a mimetic spectral element discretization for the 2D incompressible
Navier–Stokes equations that in the limit of vanishing dissipation exactly preserves mass …

Edge functions for spectral element methods

M Gerritsma - Spectral and High Order Methods for Partial Differential …, 2010‏ - Springer
It is common practice in finite element methods to expand the unknowns in nodal functions.
The discretization of the gradient, curl and divergence operators requires H 1, H (curl) and H …

Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms

A Palha, PP Rebelo, R Hiemstra, J Kreeft… - Journal of …, 2014‏ - Elsevier
This paper introduces the basic concepts for physics-compatible discretization techniques.
The paper gives a clear distinction between vectors and forms. Based on the difference …

Mimetic framework on curvilinear quadrilaterals of arbitrary order

J Kreeft, A Palha, M Gerritsma - arxiv preprint arxiv:1111.4304, 2011‏ - arxiv.org
In this paper higher order mimetic discretizations are introduced which are firmly rooted in
the geometry in which the variables are defined. The paper shows how basic constructs in …

High order geometric methods with exact conservation properties

RR Hiemstra, D Toshniwal, RHM Huijsmans… - Journal of …, 2014‏ - Elsevier
Conservation laws in, for example, electromagnetism, solid and fluid mechanics, allow an
exact discrete representation in terms of line, surface and volume integrals. In this paper, we …

Mixed mimetic spectral element method for Stokes flow: A pointwise divergence-free solution

J Kreeft, M Gerritsma - Journal of Computational Physics, 2013‏ - Elsevier
In this paper we apply the recently developed mimetic discretization method to the mixed
formulation of the Stokes problem in terms of vorticity, velocity and pressure. The mimetic …

An introduction to a compatible spectral discretization method

M Gerritsma - Mechanics of Advanced Materials and Structures, 2012‏ - Taylor & Francis
In this paper I try to explain what one means when one refers to'compatible'or'mimetic'
discretization methods. I will show why this approach is so appealing from a computational …

A discrete vector calculus in tensor grids

N Robidoux, S Steinberg - Computational Methods in Applied …, 2011‏ - degruyter.com
Mimetic discretization methods for the numerical solution of continuum mechanics problems
directly use vector calculus and differential forms identities for their derivation and analysis …