Backward Euler method for abstract time-dependent parabolic equations with variable domains
Copyright policy )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.
- University of Valladolid Spain
implicit Euler method, backward Euler method, Banach space, linear parabolic problems, Error bounds for initial value and initial-boundary value problems involving PDEs, Linear differential equations in abstract spaces, error estimates, Numerical solutions to equations with linear operators, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, time discretization
implicit Euler method, backward Euler method, Banach space, linear parabolic problems, Error bounds for initial value and initial-boundary value problems involving PDEs, Linear differential equations in abstract spaces, error estimates, Numerical solutions to equations with linear operators, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Initial value problems for second-order parabolic equations, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, time discretization
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