Comments on the fractional step method
Journal of Computational Physics
An analysis of numerical errors in large-eddy simulations of turbulence
Journal of Computational Physics
Solving diffusion equations with rough coefficients in rough grids
Journal of Computational Physics
Covolume Solutions of Three-Dimensional Div-Curl Equations
SIAM Journal on Numerical Analysis
Fully conservative higher order finite difference schemes for incompressible flow
Journal of Computational Physics
High order finite difference schemes on non-uniform meshes with good conversation properties
Journal of Computational Physics
Conservation properties of unstructured staggered mesh schemes
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
Analysis of an exact fractional step method
Journal of Computational Physics
A moving unstructured staggered mesh method for the simulation of incompressible free-surface flows
Journal of Computational Physics
Symmetry-preserving discretization of turbulent flow
Journal of Computational Physics
Discrete calculus methods for diffusion
Journal of Computational Physics
A cell-centered diffusion scheme on two-dimensional unstructured meshes
Journal of Computational Physics
High-order mimetic finite difference method for diffusion problems on polygonal meshes
Journal of Computational Physics
Mimetic finite difference method for the Stokes problem on polygonal meshes
Journal of Computational Physics
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes
Journal of Computational Physics
Journal of Computational Physics
A collocated method for the incompressible Navier-Stokes equations inspired by the Box scheme
Journal of Computational Physics
Energy-conserving Runge-Kutta methods for the incompressible Navier-Stokes equations
Journal of Computational Physics
Direct numerical simulation of turbulence using GPU accelerated supercomputers
Journal of Computational Physics
Why starting from differential equations for computational physics?
Journal of Computational Physics
Differential forms for scientists and engineers
Journal of Computational Physics
Mimetic finite difference method
Journal of Computational Physics
Hi-index | 31.50 |
A higher-order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer. Mimetic discretization methods create discrete versions of the partial differential operators (such and the gradient and divergence) that are exact in some sense and therefore mimic the important mathematical properties of their continuous counterparts. The proposed numerical method is an interesting mixture of both finite volume and finite element ideas. While the ideas presented can be applied to arbitrarily high-order accuracy, we focus in this work on the details of creating a third-order accurate method. The proposed method is shown to be exact for piecewise quadratic solutions and shows third-order convergence on arbitrary triangular/tetrahedral meshes. The numerical accuracy of the method is confirmed on both two-dimensional and three-dimensional unstructured meshes. The computational cost required for a desired accuracy is analyzed against lower-order mimetic methods.