A posteriori error estimation with the finite element method of lines for a nonlinear parabolic equation in one space dimension. (English) Zbl 0936.65113

Segeth, K.

Numer. Math. 83, No. 3, 455-475 (1999).

The present paper extends the results of recent works that investigated semidiscrete error estimation in the linear and semilinear case and fully discrete error estimation in the nonlinear case. Stronger results for convergence of a posteriori error estimates for the semidiscrete finite element method of lines for a nonlinear parabolic initial-boundary value problem are presented. The results can be used as a basis for an adaptive numerical procedure that carries out the fully discrete computation with an arbitrary time discretization.

Reviewer: Angela Handlovičová (Bratislava)

MSC:

65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K55	Nonlinear parabolic equations
65M20	Method of lines for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

nonlinear parabolic equation; semidiscrete finite element method; semidiscrete error estimation; convergence; method of lines; time discretization