Topic
Finite difference
About: Finite difference is a research topic. Over the lifetime, 19693 publications have been published within this topic receiving 408603 citations.
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TL;DR: In this article, a mixed finite element method is proposed to approximate simultaneously the pressure P and its gradient, or more generally a gradient related velocity field q in such a way that both P h and q h can be proved to converge, in adequate norms, to their continuous counterparts.
223 citations
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TL;DR: This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures, and demonstrates that different methods of implementation for the present algorithm can be deduced from a single starting point.
Abstract: This paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet.
222 citations
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TL;DR: A strategy to design locally conservative finite-difference approximations of convective derivatives for shock-free compressible flows with arbitrary order of accuracy that can be applied as a building block of low-dissipative, hybrid shock-capturing methods.
222 citations
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TL;DR: In this article, a new non-reflecting boundary scheme is proposed for time-dependent wave problems in unbounded domains, which is based on a reformulation of the sequence of NRBCs proposed by Higdon.
222 citations
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TL;DR: This study finds that polyharmonic splines (PHS) in conjunction with supplementary polynomials provide a very simple way to defeat stagnation (also known as saturation) error and give particularly good accuracy for the tasks of interpolation and derivative approximations without the hassle of determining a shape parameter.
221 citations