• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1409-1419
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• 2017

We introduce an extrapolated Crank-Nicolson characteristic finite element method to approximate solutions of a convection dominated Sobolev equation. We obtain the higher order of convergence in both the spatial direction and the temporal direction in $L^2$ normed space for the extrapolated Crank-Nicolson characteristic finite element method.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.257-270
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• 2018

An extrapolated Crank-Nicolson characteristic finite element method is introduced for approximate solutions of nonlinear Sobolev equations with a convection term. And we obtain the higher order of convergence for approximate solutions in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.795-809
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• 2001

In this paper, we apply finite element Galerkin method to a single-ohase linear Stefan problem with a forcing term. We apply the extrapolated Crank-Nicolson method to construct the fully discrete approximation and we derive optimal error estimates in the temporal direction in $L^2$, $H^1$ spaces.

• East Asian mathematical journal
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• v.26 no.5
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• East Asian mathematical journal
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• v.32 no.5
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• pp.729-744
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• 2016

A Crank-Nicolson characteristic finite element method is introduced to construct approximate solutions of a Sobolev equation with a convection term. The higher order of convergences in the temporal direction and in the spatial direction in $L^2$ normed space are verified for the Crank-Nicolson characteristic finite element method.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.773-793
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• 2001

The explicit expressions for the 2n+1 primitive idempotents in R/sub pⁿ/ = F[x]/< x/sup pⁿ/ -1>, where F is the field of prime power order q and the multiplicative order of q modulo pⁿ is ø(pⁿ)/2(n≥1 and p is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of length pⁿ, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length over GF(q)(q=2, 3, ...) are obtained.