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.
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TL;DR: In this article, the authors presented the finite difference/element method for a two-dimensional modified fractional diffusion equation, and the analysis is carried out first for the time semi-discrete scheme, and then for the full discrete scheme.
Abstract: We present the finite difference/element method for a two-dimensional modified fractional diffusion equation. The analysis is carried out first for the time semi-discrete scheme, and then for the full discrete scheme. The time discretization is based on the L1-approximation for the fractional derivative terms and the second-order backward differentiation formula for the classical first order derivative term. We use finite element method for the spatial approximation in full discrete scheme. We show that both the semi-discrete and full discrete schemes are unconditionally stable and convergent. Moreover, the optimal convergence rate is obtained. Finally, some numerical examples are tested in the case of one and two space dimensions and the numerical results confirm our theoretical analysis.
96 citations
TL;DR: A new MFD method is presented for the Stokes problem on arbitrary polygonal meshes and its stability is analyzed, which allows the method to apply to a linear elasticity problem, as well.
96 citations
TL;DR: In this paper, a solution method for the one-dimensional transient temperature and thermal stress fields in non-homogeneous materials is established, where finite element method is used to space discretize, which results in a system of first-order differential equations.
96 citations
TL;DR: This paper develops a fast alternating-direction implicit finite difference method for space-fractional diffusion equations in two space dimensions that has a significant reduction of the CPU time from more than 2 months and 1 week consumed by a traditional finite Difference method to 1.5h, using less than one thousandth of memory the standard method does.
96 citations
TL;DR: In this article, stability estimates and convergence analysis of finite difference methods for the Biot's consolidation model are presented, and central differences for space discretization and a weighed two-level time scheme are analyzed.
96 citations