A qualocation method for parabolic partial differential equations

Pani, A. K. (1999) A qualocation method for parabolic partial differential equations IMA Journal of Numerical Analysis, 19 (3). pp. 473-495. ISSN 0272-4979

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Official URL: http://imajna.oxfordjournals.org/content/19/3/473....

Related URL: http://dx.doi.org/10.1093/imanum/19.3.473


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 H1-Galerkin method in which the discretization is achieved by approximating the integrals by a composite Gauss quadrature rule. An O (h4-i) rate of convergence in the Wi.p norm for i = 0, 1 and 1 ≤ p ≤ ∞ is derived for a semidiscrete scheme without any quasi-uniformity assumption on the finite element mesh. Further, an optimal error estimate in the H2 norm is also proved. Finally, the linearized backward Euler method and extrapolated Crank-Nicolson scheme are examined and analysed.

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ID Code:81969
Deposited On:09 Feb 2012 04:42
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