Adaptive vertex-centered finite volume methods for general second-order linear elliptic partial differential equations
نویسندگان
چکیده
منابع مشابه
Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
We prove convergence of adaptive finite element methods (AFEM) for general (nonsymmetric) second order linear elliptic PDE, thereby extending the result of Morin et al [6, 7]. The proof relies on quasi-orthogonality, which accounts for the bilinear form not being a scalar product, together with novel error and oscillation reduction estimates, which now do not decouple. We show that AFEM is a co...
متن کاملFinite Difference Solution of Linear Second Order Elliptic Partial Differential Equations
u(t, 0) = 0, u(t, 1) = 1, t ≥ 0; u(0, x) = u0(x), x ∈ [0, 1]. If the initial temperature is described by the linear function u0(x) = x, x ∈ [0, 1], then the solution of the problem is u(t, x) = x, that is the temperature is independent of time. This solution is called the stationary solution of the problem. The stationary solution can be obtained by setting ∂u/∂t = 0 and solving the ordinary di...
متن کاملNON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
In this article we have considered a non-standard finite difference method for the solution of second order Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical met...
متن کاملA New Class of High Order Finite Volume Methods for Second Order Elliptic Equations
In the numerical simulation of many practical problems in physics and engineering, finite volume methods are an important and popular class of discretization methods due to the local conservation and the capability of discretizing domains with complex geometry. However they are limited by low order approximation since most existing finite volume methods use piecewise constant or linear function...
متن کاملFinite element methods for semilinear elliptic stochastic partial differential equations
We study finite element methods for semilinear stochastic partial differential equations. Error estimates are established. Numerical examples are also presented to examine our theoretical results. Mathematics Subject Classification (2000) 65N30 · 65N15 · 65C30 · 60H15
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: IMA Journal of Numerical Analysis
سال: 2018
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/dry006