A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE
نویسندگان
چکیده
Abstract We prove a-posteriori error-estimates for reduced-order modeling of quasilinear parabolic PDEs with non-monotone nonlinearity. consider the solution a semi-discrete in space equation as reference, and therefore incorporate reduced basis-, empirical interpolation-, time-discretization-errors our consideration. Numerical experiments illustrate results.
منابع مشابه
Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
It is known that the energy technique for a posteriori error analysis of finite element discretizations of parabolic problems yields suboptimal rates in the norm L∞(0, T ; L2(Ω)). In this paper we combine energy techniques with an appropriate pointwise representation of the error based on an elliptic reconstruction operator which restores the optimal order (and regularity for piecewise polynomi...
متن کاملA posteriori error estimates for non-linear parabolic equations
We consider space-time discretizations of non-linear parabolic equations. The temporal discretizations in particular cover the implicit Euler scheme and the mid-point rule. For linear equations they correspond to the well-known A-stable θ-schemes. The spatial discretizations consist of standard conforming finite element spaces that can vary from one time-level to the other. The spatial meshes m...
متن کاملA posteriori error estimates for linear parabolic equations
We consider discretizations of linear parabolic equations by A-stable θ-schemes in time and conforming finite elements in space. For these discretizations we derive a residual a posteriori error estimator. The estimator yields upper bounds on the error which are global in space and time and lower bounds that are global in space and local in time. The error estimates are fully robust in the sens...
متن کاملA Posteriori Error Estimates for Parabolic Variational Inequalities
We study a posteriori error estimates in the energy norm for some parabolic obstacle problems discretized with a Euler implicit time scheme combined with a finite element spatial approximation. We discuss the reliability and efficiency of the error indicators, as well as their localization properties. Apart from the obstacle resolution, the error indicators vanish in the so-called full contact ...
متن کاملSharply local pointwise a posteriori error estimates for parabolic problems
We prove pointwise a posteriori error estimates for semiand fullydiscrete finite element methods for approximating the solution u to a parabolic model problem. Our estimates may be used to bound the finite element error ‖u−uh‖L∞(D), where D is an arbitrary subset of the space-time domain of definition of the given PDE. In contrast to standard global error estimates, these estimators de-emphasiz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computational Optimization and Applications
سال: 2021
ISSN: ['0926-6003', '1573-2894']
DOI: https://doi.org/10.1007/s10589-021-00299-y