Convergence of an Upstream Finite
نویسنده
چکیده
We study here the discretisation of the nonlinear hyperbolic equation ut + div(vf(u)) = 0 in IR 2 IR+, with given initial condition u(:; 0) = u0(:) in IR 2 , where v is a function from IR 2 IR+ to IR 2 such that divv = 0 and f is a given nondecreasing function from IR to IR. An explicit Euler scheme is used for the time discretisation of the equation, and a triangular mesh for the spatial discretisation. Under a usual stability condition, we prove the convergence of the solution given by an upstream nite volume scheme towards the unique entropy weak solution to the equation.
منابع مشابه
Numerical Investigation on Compressible Flow Characteristics in Axial Compressors Using a Multi Block Finite Volume Scheme
An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was employed and it was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Monotonic Upstream Scheme for Conservat...
متن کاملConvergence of a finite volume scheme for an elliptic-hyperbolic system
We study here the convergence of a finite volume scheme for a coupled system of an hyperbolic and an elliptic equations defined on an open bounded set of IR. On the elliptic equation, a four points finite volume scheme is used then an error estimate on a discrete H norm of order h is proved, where h defines the size of the triangulation. On the hyperbolic equation, one uses an upstream scheme w...
متن کاملThe Performance of an Hexahedron C* Element in Finite Element Analysis
The performance of an 8-noded hexahedron C1* element in elasticity is investigated. Three translational displacements and their derivatives as strain in each direction are considered as degrees of freedom (d.o.f.’s) at each node. The geometric mapping is enforced using a C0 element with no derivative as nodal d.o.f.’s . The stiffness matrix of the element is also computed using a transformation...
متن کاملConvergence theorems of an implicit iteration process for asymptotically pseudocontractive mappings
The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.
متن کاملNonlinear Guidance Law with Finite Time Convergence Considering Control Loop Dynamics
In this paper a new nonlinear guidance law with finite time convergence is proposed. The second order integrated guidance and control loop is formulated considering a first order control loop dynamics. By transforming the state equations to the normal form, a finite time stabilizer feedback linearization technique is proposed to guarantee the finite time convergence of the system states to zero...
متن کاملStrong convergence theorem for finite family of m-accretive operators in Banach spaces
The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1993