A Fundamental Solution for a Biharmonic Finite-Difference Operator1
نویسنده
چکیده
منابع مشابه
Convergence Analysis of a Quadrature Finite Element Galerkin Scheme for a Biharmonic Problem
A quadrature finite element Galerkin scheme for a Dirichlet boundary value problem for the biharmonic equation is analyzed for a solution existence, uniqueness, and convergence. Conforming finite element space of Bogner-Fox-Schmit rectangles and an integration rule based on the two-point Gaussian quadrature are used to formulate the discrete problem. An H2-norm error estimate is obtained for th...
متن کاملA finite difference method for the smooth solution of linear Volterra integral equations
The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...
متن کاملHigh Accuracy and Multiscale Multigrid Computation for Three Dimensional Biharmonic Equations
The multiscale multigrid method is presented in this article to solve the linear systems arising from a fourth order discretisation. We used a symbolic algebra packageMathematica to derive a family of finite difference approximations on a 27 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at selected grid points. A set of test problems are presente...
متن کاملFinite volume schemes for the biharmonic problem on general meshes
During the development of a convergence theory for Nicolaides’ extension [21, 24] of the classical MAC scheme [25, 22, 26] for the incompressible Navier-Stokes equations to unstructured triangle meshes, it became clear that a convergence theory for a new kind of finite volume discretizations for the biharmonic problem would be a very useful tool in the convergence analysis of the generalized MA...
متن کاملA fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow
Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary condi...
متن کامل