A finite element method adaptive in space and time for nonlinear reaction-diffusion systems

DOI10.1016/0899-8248(92)90004-RzbMath0796.65104OpenAlexW1973232334MaRDI QIDQ4036025

Jens Lang, Artur Walter

Publication date: 16 May 1993

Published in: IMPACT of Computing in Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0899-8248(92)90004-r

zbMATH Keywords

plasmafinite element methodabstract Cauchy problemHilbert spacecombustionelectrodynamicsreaction-diffusion equationstime discretizationecologyflame propagationlinear basis functionsRunge- Kutta methodstheory of analytic semigroups

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Nonlinear differential equations in abstract spaces (34G20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solutions to equations with nonlinear operators (65J15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (7)

Three new approaches for solving a class of strongly nonlinear two-point boundary value problems ⋮ Two-dimensional fully adaptive solutions of reaction-diffusion equations ⋮ A moving collocation method for solving time dependent partial differential equations ⋮ Adaptive finite element simulation of the time-dependent simplified \(P_N\) equations ⋮ A linearly implicit predicator-corrector method for reaction-diffusion equations ⋮ Two-dimensional cascadic finite element computations of combustion problems ⋮ Continuous and discontinuous Galerkin methods with finite elements in space and time for parallel computing of viscoelastic deformation

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