A qualocation method for parabolic partial differential equations

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A qualocation method for parabolic partial differential equations

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Title: A qualocation method for parabolic partial differential equations
Author: PANI, AK
Abstract: In this paper a qualocation method is analysed for parabolic partial differential equations in one space dimension. This method may be described as a discrete HI-Galerkin method in which the discretization is achieved by approximating the integrals by a composite Gauss quadrature rule. An O(h(4-i)) rate of convergence in the W-i,W-p norm for i = 0, 1 and 1 less than or equal to p less than or equal to infinity is derived for a semidiscrete scheme without any quasi-uniformity assumption on the finite element mesh. Further, an optimal error estimate in the H-2 norm is also proved. Finally, the linearized backward Euler method and extrapolated Crank-Nicolson scheme are examined and analysed.
URI: http://dx.doi.org/10.1093/imanum/19.3.473
http://dspace.library.iitb.ac.in/xmlui/handle/10054/10339
http://hdl.handle.net/10054/10339
Date: 1999


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