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Adaptive space‐time finite element solvers for parabolic initial‐boundary value problems with non‐smooth solutions
Author(s) -
Langer Ulrich,
Schafelner Andreas
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900305
Subject(s) - a priori and a posteriori , polygon mesh , finite element method , mathematics , space (punctuation) , boundary value problem , mathematical analysis , spacetime , parabolic partial differential equation , residual , space time , boundary (topology) , mathematical optimization , computer science , algorithm , partial differential equation , geometry , physics , philosophy , epistemology , quantum mechanics , operating system , chemical engineering , engineering , thermodynamics
We consider conforming finite element schemes on completely unstructured simplicial space‐time meshes for the numerical solution of non‐autonomous parabolic problems with coefficients that may discontinuously depend on the space and time variables. We present a priori estimates for low‐regularity solutions. We compare two adaptive procedures that are based on residual and functional a posteriori error indicators.