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Finite Element Methods for Semilinear Parabolic Initial、Boundary Value Problems with Singularities

Author: HanYuTao
Tutor: LiDeMao
School: Inner Mongolia University
Course: Applied Mathematics
Keywords: Singular semi- linear parabolic equations Weighted Sobolev spaces Existence and uniqueness of the generalized solution Weighted L2 norm estimates Linearization correction
CLC: O241.82
Type: Master's thesis
Year: 2004
Downloads: 35
Quote: 1
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Abstract


Elliptic and parabolic partial differential equations with a singular coefficient is a very important equation , the last ten years , Computational Mathematics workers using finite difference , finite element method to such issues , in-depth study and get good results. In this paper, we consider the beginning of a class of singular semilinear parabolic equations , boundary value problem of the finite element method . First , the original equation linearization , and prove the existence and uniqueness of the generalized solution of the corresponding variational problem . Then given respectively the weighted L semi- discrete and fully discrete solution 2 norm error estimates . Finally, consider the linearization correction symmetrical Crank-Nicolson-Galerkin finite element method .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
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