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Abstract
We consider a Galerkin procedure to solve a parabolic integrodifferential equation that arises in a gas combustion model. This model has been proposed by Kassoy and Poland, and subsequently analyzed by Bebernes, Eberly and Bressan. The problem is formulated in the variational form. In order to estimate the error, some intermediate projection has been employed. Under certain conditions on the given data, the error estimate has been obtained. A fully descretized version by using an extrapolated Crank-Nicolson method has been applied and the order of convergence derived.
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References
- BEBERNES, J. and BRESSAN, A. 1982. Thermal behaviour for a confined reactive gas. J. Diff. Equations, 44: 118-133.
- BEBERNES, J. and BRESSAN, A. 1988. Total blowup versus single point blowup. J. Diff. Equations, 73(1): 30-44.
- BEBERNES, J. and EBERLY, D. 1989. Mathematical problems from combustion theory. Applied Mathematics Series, vol. 83, Springer-Verlag, New York.
- BEBERNES, J., BRESSAN, A., KASSOY, D. and RILEY, N. 1989. The confined non-diffusive thermal explosion with spatially homogeneous pressure variation. Comb. Sci. Tech., 63: 45-62.
- CANNON, J. and LIN, Y-P. 1990a. A Galerkin procedure for diffusion equations with integral boundary conditions. Int. J. Engng. Sci., 28(7): 579-587.
- CANNON, J. and LIN, Y-P. 1990b. A priori error estimates for finite element methods for nonlinear diffusion equations with memory. SIAM J. Numer. Anal., 27(3): 595-607.
- GILBARG, D. and TRUDINGER, N.S. 1983. Elliptic Partial Differential Equations of Second Order. Springer-Verlag.
- KASSOY, D. and POLAND, J. 1983. The induction period of a thermal explosion in a gas between infinite parallel plates. Combustion and Flame, 50: 259-274.
- THOMÉE, V. 2006. Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, Springer-Verlag New York, USA.
References
BEBERNES, J. and BRESSAN, A. 1982. Thermal behaviour for a confined reactive gas. J. Diff. Equations, 44: 118-133.
BEBERNES, J. and BRESSAN, A. 1988. Total blowup versus single point blowup. J. Diff. Equations, 73(1): 30-44.
BEBERNES, J. and EBERLY, D. 1989. Mathematical problems from combustion theory. Applied Mathematics Series, vol. 83, Springer-Verlag, New York.
BEBERNES, J., BRESSAN, A., KASSOY, D. and RILEY, N. 1989. The confined non-diffusive thermal explosion with spatially homogeneous pressure variation. Comb. Sci. Tech., 63: 45-62.
CANNON, J. and LIN, Y-P. 1990a. A Galerkin procedure for diffusion equations with integral boundary conditions. Int. J. Engng. Sci., 28(7): 579-587.
CANNON, J. and LIN, Y-P. 1990b. A priori error estimates for finite element methods for nonlinear diffusion equations with memory. SIAM J. Numer. Anal., 27(3): 595-607.
GILBARG, D. and TRUDINGER, N.S. 1983. Elliptic Partial Differential Equations of Second Order. Springer-Verlag.
KASSOY, D. and POLAND, J. 1983. The induction period of a thermal explosion in a gas between infinite parallel plates. Combustion and Flame, 50: 259-274.
THOMÉE, V. 2006. Galerkin Finite Element Methods for Parabolic Problems. Springer Series in Computational Mathematics, Springer-Verlag New York, USA.