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On the immersed boundary method: Finite element versus finite volume approach
Computers & Fluids, 2012A projection approach is presented for the coupled system of time-dependent incompressible Navier-Stokes equations in conjunction with the Immersed Boundary Method (IBM) for solving fluid flow problems in the presence of rigid objects not represented by the underlying mesh. The IBM allows solving the flow for geometries with complex objects without the
Frisani, Angelo, Hassan, Yassin A.
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Fundamentals of Finite Element and Finite Volume Methods
2018There are three distinct methods of numerical solution techniques: finite difference, finite volume and finite element methods. The purpose in each is to convert the differential equations into algebraic equations. The main differences between the three methods are associated with the way the differential equations are converted to algebraic equations.
C. Ranganayakulu +1 more
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The finite volume element method for a parameter identification problem
Journal of Ambient Intelligence and Humanized Computing, 2014In this paper we use finite volume element method to solve a parameter identification problem of parabolic equations with overspecified-data. We provide the numerical scheme of the unknown function and control parameters and obtain the error estimates of approximate solution.
Zhiguang Xiong +4 more
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Finite Element and Finite Volume Methods
2009In this chapter we consider finite element and finite volume discretisations of $$Lu\,: = - \varepsilon u'' - bu' + cu = f\,\,{\rm in}\,(0,1), \,\,\ u(0) = u (1) = 0,$$ with b ≥ β > 0. Its associated variational formulation is: Find \(u \in H_0^1 (0,1)\) such that $$a(u, v) = f(v)\,\,\, {\rm for\, all}\,\, v \in H_0^1 (0,1),$$ (5.2 ...
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Finite volume element method with Lagrangian cubic functions
Journal of Systems Science and Complexity, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yuqiong Ding, Yonghai Li
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Combined finite volume–finite element method for shallow water equations
Computers & Fluids, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, JiWen, Liu, RuXun
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The finite volume element method with quadratic basis functions
Computing, 1996A box method with quadratic basis functions is considered for the Dirichlet problem for the Poisson equation in polygon regions. The resulting grid systems are specified for square grid triangulations and more general ones. It should be noted that the corresponding matrices are non-symmetrical.
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The finite volume element methods for Poisson equation based on Adini’s element
Applied Mathematics and Computation, 2013In this paper, we construct and analyze the finite volume element scheme based on Adini's element for Poisson equation, choosing trial and test spaces as the Adini's finite element space and the piecewise linear function space respectively. Optimal order error estimates in H^1 and L^2 norms are derived.
Changhua Yu, Yanhe Wang, Yonghai Li
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Superconvergence of finite volume element method for elliptic problems
Advances in Computational Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Rectangular Finite Volume Element Method for a Semilinear Elliptic Equation
Journal of Scientific Computing, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhiguang Xiong, Yanping Chen 0002
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