Zusammenfassung
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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