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Adaptivity with dynamic meshes for space-time finite element discretizations of parabolic equations. (English) Zbl 1169.65098
The paper deals with the numerical solution of parabolic partial differential equations. The authors develop an error estimator and an adaptive algorithm for efficient solution. The error estimator assesses the discretization error with respect to a given quantity of physical interest and separates the influence of the time and space discretizations. This allows to set up an efficient adaptive strategy producing refined meshes for each time step and an adapted time discretization. The space and time discretization errors are equilibrated, leading to an efficient method. A description of the numerical implementation is presented and finally two numerical experiments demonstrating the efficiency of the method are included.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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