A posteriori error estimates and grid adjustment for a nonlinear parabolic equation

K. Segeth

Mathematics and Computers in Simulation (MATCOM), 1999, vol. 50, issue 1, 331-338

Abstract: The paper is concerned with a posteriori error estimates needed for the adaptive construction of a space grid in solving an initial-boundary value one-dimensional problem for a nonlinear parabolic partial differential equation by the method of lines. A posteriori error indicators are introduced and studied for the semidiscrete case, and the statement on their convergence rate is presented. Under certain conditions, it adds some more results to those of Moore [SIAM J. Numer. Anal. 31 (1994) 149–164] who treats only a linear equation in the semidiscrete case. Complete statements including proofs will appear as a paper [K. Segeth, A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension, to appear].

Keywords: A posteriori error estimate; Nonlinear parabolic equation; Finite element method; Method of lines (search for similar items in EconPapers)
Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:50:y:1999:i:1:p:331-338

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