Design and Convergence Analysis for an Adaptive Discretization of the Heat Equation
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IMA J. Numer. Anal. doi:10.1093/imanum/drr026, (2012)Online First.

We derive an algorithm for the adaptive approximation of solutions to parabolic equations. It is based on adaptive finite elements in space and the implicit Euler discretization in time with adaptive time-step sizes. We prove that, given a positive tolerance for the error, the adaptive algorithm reaches the final time with a space�time error between continuous and discrete solution that is below the given tolerance. Numerical experiments reveal a more than competitive performance of our algorithm ASTFEM (adaptive space�time finite element method).
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