Two-Level a Posteriori Error Estimation for Adaptive Multilevel Stochastic Galerkin Finite Element Method
نویسندگان
چکیده
The paper considers a class of parametric elliptic partial differential equations (PDEs), where the coefficients and right-hand side function depend on infinitely many (uncertain) parameters. W...
منابع مشابه
A posteriori error estimation for the stochastic collocation finite element method
In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variables. We derive a residual-based a posteriori error estimate that is constituted of two parts controlling the stochastic collocation (SC) and t...
متن کاملA Two-dimensional r-Adaptive Finite Element Method Based on A Posteriori Error Estimates
An r-adaptive nite element method based on moving mesh PDEs and a posteri-ori error estimates is presented. The error estimation is done by applying a technique developed by Bank and Weiss to elliptic diierential equations which result here from temporal discretization of the underlying physical PDEs on moving meshes. Construction of the monitor function based on the error estimate is discussed...
متن کاملA Posteriori Finite Element Error Estimation for Diffusion Problems
Adjerid et al. 2] and Yu 19, 20] show that a posteriori estimates of spatial discretiza-tion errors of piecewise bi-p polynomial nite element solutions of elliptic and parabolic problems on meshes of square elements may be obtained from jumps in solution gradients at element vertices when p is odd and from local elliptic or parabolic problems when p is even. We show that these simple error esti...
متن کاملA Posteriori Error Estimation for Adaptive Iga Boundary Element Methods
A posteriori error estimation and adaptive mesh-refinement are well-established and important tools for standard boundary element methods (BEM) for polygonal boundaries and piecewise polynomial ansatz functions (see e.g. the seminal work [1] for the derivation of the weighted-residual error estimator and [5] for convergence even with optimal rates). In contrast, the mathematically reliable a po...
متن کاملA posteriori error estimate for the mixed finite element method
A computable error bound for mixed finite element methods is established in the model case of the Poisson–problem to control the error in the H(div,Ω) ×L2(Ω)–norm. The reliable and efficient a posteriori error estimate applies, e.g., to Raviart–Thomas, Brezzi-Douglas-Marini, and Brezzi-DouglasFortin-Marini elements. 1. Mixed method for the Poisson problem Mixed finite element methods are well-e...
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: SIAM/ASA Journal on Uncertainty Quantification
سال: 2021
ISSN: ['2166-2525']
DOI: https://doi.org/10.1137/20m1342586