Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation [PDF]
Advances in Difference Equations, 2007 The numerical solution of partial differential equations with finite differences mimetic methods that satisfy properties of the continuum differential operators and mimic discrete versions of appropriate integral identities is more likely to produce ...
Rojas S +3 more
doaj +4 more sources
A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods [PDF]
Mathematical Models and Methods in Applied Sciences, 2008 We investigate the connections between several recent methods for the discretization of anisotropic heterogeneous diffusion operators on general grids.
Eymard R. +4 more
core +9 more sources
A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems [PDF]
Computers & Mathematics with Applications, 2014 We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to achieve ...
Antonietti, Paola F. +2 more
core +6 more sources
Results in Applied Mathematics, 2022 The Black–Scholes differential operator which underlies the option pricing of European and American options is known to be degenerate close to the boundary at zero.
David Sena Attipoe, Antoine Tambue
doaj +1 more source
Physics-Capturing Discretizations for Spectral Wind-Wave Models
Fluids, 2021 This paper discusses the discretization methods that have been commonly employed to solve the wave action balance equation, and that have gained a renewed interest with the widespread use of unstructured grids for third-generation spectral wind-wave ...
Marcel Zijlema
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Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes [PDF]
, 2014 Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that approximate constitutive
Bonelle, Jerome, Ern, Alexandre
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Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection [PDF]
, 2013 Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead to a ...
Paulino, Glaucio H., Talischi, Cameron
core +1 more source
Oil & Gas Science and Technology, 2017 Nowadays, some frameworks like Arcane and Dune offer a number of advanced tools to deal with the complexity related to parallelism, meshes and linear solvers.
Gratien Jean-Marc
doaj +1 more source
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study [PDF]
, 2016 It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the ...
Antonietti, Paola F. +3 more
core +2 more sources
Numerical analysis for the pure Neumann control problem using the gradient discretisation method
, 2017 The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that directly applies to a
Droniou, Jerome +2 more
core +2 more sources