On C. Neumann's Method for Second-Order Elliptic Systems in Domains with Non-smooth Boundaries
نویسندگان
چکیده
منابع مشابه
On the Hadamard Formula for Second Order Systems in Non-Smooth Domains
Perturbations of eigenvalues of the Dirichlet problem for a second order elliptic system in a bounded domain Ω in R are studied under variations of the domain Ω. We investigate the case when the perturbed domain is located in a d-neighborhood of the reference Lipschitz domain. A new asymptotic formula is derived; it contains terms that are absent in the classical formula of Hadamard. The latter...
متن کاملAugmented high order finite volume element method for elliptic PDEs in non-smooth domains: Convergence study
1. Background The Finite Volume ElementMethod (FVEM) is a numerical method for approximating the solution of a partial differential equation (PDE) in a trial function space spanned by piecewise polynomial basis functions, similar to the Finite Element Method (FEM). The coefficients of the linear combination of the basis functions are obtained by imposing the PDE through integrations over contro...
متن کاملA second order virtual node method for elliptic problems with interfaces and irregular domains
We present a second order accurate, geometrically flexible and easy to implement method for solving the variable coefficient Poisson equation with interfacial discontinuities or on irregular domains, handling both cases with the same approach. We discretize the equations using an embedded approach on a uniform Cartesian grid employing virtual nodes at interfaces and boundaries. A variational me...
متن کاملNumerical solution of second-order elliptic equations on plane domains
— The paper présents a gênerai discretization method for convective diffusion équations. The schemes are hased on an intégral formula and have the following advantages : 1. They are effective particularly in the case when convection is dominated ; 2. Solutions obtained by them satisfy a discrete conservation law ; 3. A discrete maximum principle is valid. We show that the fïnite element solutio...
متن کاملGreen’s Matrices of Second Order Elliptic Systems with Measurable Coefficients in Two Dimensional Domains
Gi j(·, y) = 0 on ∂Ω ∀y ∈ Ω, where δik is the Kronecker delta symbol and δy(·) is the Dirac delta function with a unit mass at y. In the scalar case (i.e., when N = 1), the Green’s matrix becomes a real valued function and is usually called the Green’s function. We prove that if Ω has either finite volume or finite width, then there exists a unique Green’s matrix in Ω; see Theorem 2.12. The sam...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2001.7615