Backward Euler method for abstract time-dependent parabolic equations with variable domains
For linear parabolic problems with time-dependent operator, the temporal discretization by means of the implicit Euler method is studied in an abstract Banach space setting. This covers also problems with time-dependent non-homogeneous right-hand side and boundary conditions. The author proves new general results in the situation of operators with time-dependent domain of definition. Error estimates are obtained for sufficiently smooth exact solutions and operators being Hölder continuous. Finally, the author shows how classical problems meet the new framework.
scientific article; zbMATH DE number 1356179