Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived and the first order convergence rate and the second-order convergence rate for the pressure are demonstrated with numerical experiments.
Abstract: New mimetic discretizations of diffusion-type equations (for instance, equations modeling single phase Darcy flow in porous media) on unstructured polygonal meshes are derived. The first order convergence rate for the fluid velocity and the second-order convergence rate for the pressure on polygonal, locally refined and non-matching meshes are demonstrated with numerical experiments.
118 citations
TL;DR: In this article, a general relation between a sampled point and its nearby points is derived and the derived relation and the generalized Douglas scheme are extended to fourth order accuracy irrespective of the existence of the step-index interfaces.
Abstract: A general relation, considering the interface conditions, between a sampled point and its nearby points is derived. Making use of the derived relation and the generalized Douglas scheme, the three point formulas in the finite-difference modeling of step-index optical devices are extended to fourth order accuracy irrespective of the existence of the step-index interfaces. With numerical analysis and numerical assessment, several frequently used formulas are investigated.
117 citations
TL;DR: A finite difference technique on rectangular cell-centered grids with local refinement is proposed in order to derive discretizations of second-order elliptic equations of divergence type approximating the so-called balance equa1 1/2 tion.
Abstract: A finite difference technique on rectangular cell-centered grids with local refinement is proposed in order to derive discretizations of second-order elliptic equations of divergence type approximating the so-called balance equa1 1/2 tion. Error estimates in a discrete H -norm are derived of order h ' for a simple symmetric scheme, and of order h ' for both a nonsymmetric and a more accurate symmetric one, provided that the solution belongs to H +a for a > \\ and a > \\ , respectively.
117 citations
TL;DR: The formulation combines the primitive function approach with five-point spatially sixth- and fourth-order methods to develop a fully discrete scheme for linear wave propagation phenomena with particular emphasis on computational electromagnetics in the time-domain.
117 citations
TL;DR: In this article, high order essentially non-oscillatory (ENO) finite difference schemes are applied to the 2D and 3D compressible Euler and Navier-Stokes equations.
117 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |