Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation
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 +3 more sources
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 ...
Cameron Talischi, G. Paulino
semanticscholar +4 more sources
The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences [PDF]
SIAM Journal of Control and Optimization, 2016 In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretization method.
J. Droniou, N. Nataraj, D. Shylaja
semanticscholar +1 more source
Selecciones Matemáticas, 2021 Numerical methods are useful for solving differential equations that model physical problems, for example, heat transfer, fluid dynamics, wave propagation, among others; especially when these cannot be solved by means of exact analysis techniques, since ...
Abdul Abner Lugo Jiménez +2 more
semanticscholar +1 more source
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
core +6 more sources
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
Introduction to discrete functional analysis techniques for the numerical study of diffusion equations with irregular data [PDF]
, 2015 We give an introduction to discrete functional analysis techniques for stationary and transient diffusion equations. We show how these techniques are used to establish the convergence of various numerical schemes without assuming non-physical regularity ...
Droniou, Jerome
core +3 more sources
A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems [PDF]
, 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 +3 more sources
Enforcing the non-negativity constraint and maximum principles for diffusion with decay on general computational grids [PDF]
, 2010 In this paper, we consider anisotropic diffusion with decay, and the diffusivity coefficient to be a second-order symmetric and positive definite tensor.
Arnold +65 more
core +1 more source
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