Results 1 to 10 of about 263,258 (175)
Mimetic finite differences for elliptic problems [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2009 In multi-physics codes used adaptive mesh refinement techniques and other special requirements for the solution of partial differential equations results in polyhedral meshes with possible degenerate elements. In comparison to other grids polyhedral meshes can improve the adaption of the grid to special requirements of the numerical solution and can ...
F. Brezzi, A. Buffa, K. Lipnikov
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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
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The Mimetic Methods Toolkit: An object-oriented API for Mimetic Finite Differences
Journal of Computational and Applied Mathematics, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
E. Sanchez, C. Paolini, J. Castillo
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Superconvergence of the Velocity in Mimetic Finite Difference Methods on Quadrilaterals [PDF]
SIAM Journal on Numerical Analysis, 2005 Summary: Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over \(h^2\)-uniform quadrilateral meshes. The superconvergence holds for a full tensor coefficient. The analysis exploits a relation between mimetic finite differences and mixed finite element methods via a special ...
M. Berndt +4 more
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Advances in Water Resources, 2020 We explore the coupling of surface and subsurface flows on fully unstructured meshes that conform to complex soil structures. To accommodate the distorted meshes that inevitably result from explicit representation of complex soil structures, we leverage ...
E. Coon +7 more
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Mimetic finite differences for nonlinear and control problems
Mathematical Models and Methods in Applied Sciences, 2014 In this paper we review some recent applications of the mimetic finite difference method to nonlinear problems (variational inequalities and quasilinear elliptic equations) and optimal control problems governed by linear elliptic partial differential equations. Several numerical examples show the effectiveness of mimetic finite differences in building
P. Antonietti +3 more
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Applied Mathematics and Computation, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Attipoe Sena, David, Tambue, Antoine
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A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell's Equations [PDF]
SIAM Journal on Scientific Computing, 2021 Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical properties.
James H. Adler +3 more
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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
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Local flux mimetic finite difference methods [PDF]
Numerische Mathematik, 2008 The authors use a MFPA-type construction to develop new cell-centered discretization methods on polyhedral meshes for diffusion problems with full tensor coefficients. Under a few constructive assumptions they prove first-order convergence for both the velocity and the pressure variables, as well as second-order superconvergence for the pressure ...
Lipnikov, Konstantin +2 more
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