79 citations · 295 across the 22 of their papers we have counts for
22 papers · 1 filter
Decoupled structure-preserving discretization of incompressible MHD equations with general boundary conditions
Yi Zhang, Artur Palha, Andrea Brugnoli +2
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is pro…
A MEEVC discretization for two-dimensional incompressible Navier-Stokes equations with general boundary conditions
Yi Zhang, Artur Palha, Marc Gerritsma +1
In this work, we introduce a mass, energy, enstrophy and vorticity conserving (MEEVC) mixed finite element discretization for two-dimensional incompressible Navier-Stokes equations…
Use of algebraic dual representations in domain decomposition methods for Darcy flow in 3D domain
V. Jain, A. Palha, M. Gerritsma
In this work we use algebraic dual representations in conjunction with domain decomposition methods for Darcy equations. We define the broken Sobolev spaces and their finite dimens…
Estimation and numerical validation of inf-sup constant for bilinear form (p, div u)
V. Jain, M. Gerritsma
We give a derivation for the value of inf-sup constant for the bilinear form (p, div u). We prove that the value of inf-sup constant is equal to 1.0 in all cases and is independent…
A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains
Yi Zhang, Artur Palha, Marc Gerritsma +1
We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization…
A conservative, physically compatible, dual-field discretization for turbidity currents: with application to the lock-exchange problem
Gonzalo G. de Diego, Artur Palha, Marc Gerritsma
In this work we present a structure preserving discretization for turbidity currents based on a mass-, energy-, enstrophy-, and vorticity-conserving formulation for 2D incompressib…
A conservative hybrid method for Darcy flow
Varun Jain, Yi Zhang, Joël Fisser +2
We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for 1) conservation of mass, and 2) inter-element continuity, are topological…
Algebraic dual polynomials for the equivalence of curl-curl problems
Marc Gerritsma, Varun Jain, Yi Zhang +1
In this paper we will consider two curl-curl equation in two dimensions. One curl-curl problem for a scalar quantity and one problem for a vector field . For Dirichlet…
Mimetic Spectral Element Method for Anisotropic Diffusion
Marc Gerritsma, Artur Palha, Varun Jain +1
This paper addresses the topological structure of steady, anisotropic, inhomogeneous diffusion problems. Two discrete formulations: a) mixed and b) direct formulations are discusse…
Construction and application of algebraic dual polynomial representations for finite element methods on quadrilateral and hexahedral meshes
Varun Jain, Yi Zhang, Artur Palha +1
Given a sequence of finite element spaces which form a de Rham sequence, we will construct a dual representation of these spaces with associated differential operators which connec…
Discrete conservation properties for shallow water flows using mixed mimetic spectral elements
David Lee, Artur Palha, Marc Gerritsma
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functi…
A Higher Order Equilibrium Finite Element Method
K. Olesen, B. Gervang, J. N. Reddy +1
In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surfac…
A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations
Artur Palha, Marc Gerritsma
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 mas…
Mimetic spectral element method for Hamiltonian systems
Artur Palha, Marc Gerritsma
There is a growing interest in the conservation of invariants when numerically solving a system of ordinary differential equations. Methods that exactly preserve these quantities i…
A Geometric Approach Towards Momentum Conservation
D. Toshniwal, R. H. M. Huijsmans, M. I. Gerritsma
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we tre…
Mimetic Spectral Element advection
Artur Palha, Pedro Pinto Rebelo, Marc Gerritsma
We present a discretization of the linear advection of differential forms on bounded domains. The framework previously established is extended to incorporate the Lie derivative, $\…
Physics-compatible discretization techniques on single and dual grids, with application to the Poisson equation of volume forms
Artur Palha, Pedro Pinto Rebelo, René Hiemstra +2
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 be…
Mixed Mimetic Spectral Element method applied to Darcy's problem
Pedro Pinto Rebelo, Artur Palha, Marc Gerritsma
We present a discretization for Darcy's problem using the recently developed Mimetic Spectral Element Method. The gist lies in the exact discrete representation of integral relatio…
High order gradient, curl and divergence conforming spaces, with an application to NURBS-based IsoGeometric Analysis
R. R. Hiemstra, R. H. M. Huijsmans, M. I. Gerritsma
Conservation laws, in for example, electromagnetism, solid and fluid mechanics, allow an exact discrete representation in terms of line, surface and volume integrals. We develop hi…
A priori error estimates for compatible spectral discretization of the Stokes problem for all admissible boundary conditions
Jasper Kreeft, Marc Gerritsma
This paper describes the recently developed mixed mimetic spectral element method for the Stokes problem in the vorticity-velocity-pressure formulation. This compatible discretizat…
Mixed Mimetic Spectral Element Method for Stokes Flow: A Pointwise Divergence-Free Solution
Jasper Kreeft, Marc Gerritsma
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…
Mimetic framework on curvilinear quadrilaterals of arbitrary order
Jasper Kreeft, Artur Palha, Marc Gerritsma
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 i…