Previous |  Up |  Next


parabolic problem; a-posteriori error estimate
The aim of the paper is to derive a method for the construction of a-posteriori error estimate to approximate solutions to parabolic initial-boundary value problems. The computation of the suggested error bound requires only the computation of a finite number of systems or linear algebraic equations. These systems can be solved parallelly. It is proved that the suggested a-posteriori error estimate tends to zero if the approximation tends to the true solution.
[1] Eriksson K., Johnson C.: Adaptive finite element methods for parabolic problems I: A linear model problem. SIAM J. Numer. Anal. 28 (1991), 43-77. MR 1083324 | Zbl 0732.65093
[2] Gajewski H., Gröger K.: Konjugierte Probleme und a-posteriori Fehlerabschätzungen. Math. Nachrichten 73 (1976), 315-333. MR 0435959
[3] Gajewski H., Gröger K., Zacharias K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie -Verlag Berlin, 1974 (Russian Mir Moskva 1978). MR 0636412
[4] Weisz J.: A posteriori error estimate of approximate solutions to a mildly nonlinear elliptic boundary value problem. Commentationes Math. Univ. Carolinae 31 (1990), 315-322. MR 1077902 | Zbl 0709.65074
Partner of
EuDML logo