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Title: Enabling Predictive Simulation and UQ of Complex Multiphysics PDE Systems by the Development of Goal-Oriented Variational Sensitivity Analysis and A Posteriori Error Estimation Methods

it was demonstrated that a posteriori analyses in general and in particular one that uses adjoint methods can accurately and efficiently compute numerical error estimates and sensitivity for critical Quantities of Interest (QoIs) that depend on a large number of parameters. Activities include: analysis and implementation of several time integration techniques for solving system of ODEs as typically obtained from spatial discretization of PDE systems; multirate integration methods for ordinary differential equations; formulation and analysis of an iterative multi-discretization Galerkin finite element method for multi-scale reaction-diffusion equations; investigation of an inexpensive postprocessing technique to estimate the error of finite element solution of the second-order quasi-linear elliptic problems measured in some global metrics; investigation of an application of the residual-based a posteriori error estimates to symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems; a posteriori analysis of explicit time integrations for system of linear ordinary differential equations; derivation of accurate a posteriori goal oriented error estimates for a user-defined quantity of interest for two classes of first and second order IMEX schemes for advection-diffusion-reaction problems; Postprocessing finite element solution; and A Bayesian Framework for Uncertain Quantification of Porous Media Flows.
Publication Date:
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Technical Report
Research Org:
University of Wyoming
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States