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Keywords:
a posteriori error estimate; system of parabolic equations; finite element method; method of lines
a posteriori error estimate; system of parabolic equations; finite element method; method of lines
Summary:
Systems of parabolic differential equations are studied in the paper. Two a posteriori error estimates for the approximate solution obtained by the finite element method of lines are presented. A statement on the rate of convergence of the approximation of error by estimator to the error is proved.
References:
[1] S. Adjerid, J.E. Flaherty: A moving finite element method with error estimation and refinement for one-dimensional time dependent partial differential equations. SIAM J. Numer. Anal. 23 (1986), 778–796. DOI 10.1137/0723050 | MR 0849282
[2] S. Adjerid, J.E. Flaherty, Y.J. Wang: A posteriori error estimation with finite element methods of lines for one-dimensional parabolic systems. Numer. Math. 65 (1993), 1–21. DOI 10.1007/BF01385737 | MR 1217436
[3] I. Babuška, W.C. Rheinboldt: A posteriori error estimates for the finite element method. Internat. J. Numer. Methods Engrg. 12 (1978), 1597–1615. DOI 10.1002/nme.1620121010
[4] M. Bieterman, I. Babuška: The finite element method for parabolic equations I, II. Numer. Math. 40 (1982), 339–371, 373–406. DOI 10.1007/BF01396451
[5] F.R. Gantmacher: Matrix Theory. Moskva, Nauka, 1966. (Russian)
[6] A.C. Hindmarsh: LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM SIGNUM Newsletter 15 (1980), 10–11. DOI 10.1145/1218052.1218054
[7] J.T. Oden, G.F. Carey: Finite Elements: Mathematical Aspects, Vol. 4. Englewood Cliffs, NJ, Prentice-Hall, 1983. MR 0767804
[8] L.R. Petzold: A Description of DDASSL: A Differential/Algebraic System Solver. Sandia Report No. Sand 82-8637, Livermore, CA, Sandia National Laboratory, 1982. MR 0751605
[9] B. Szabo, I. Babuška: Finite Element Analysis. New York, J. Wiley & Sons, 1991. MR 1164869
[10] V. Thomée: Negative norm estimates and superconvergence in Galerkin methods for parabolic problems. Math. Comp. 34 (1980), 93–113. DOI 10.2307/2006222 | MR 0551292
[11] R. Wait, A.R. Mitchell: Finite Element Analysis and Applications. Chichester, J. Wiley & Sons, 1985. MR 0817440
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