Varis Carey

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In this paper, we perform an a posteriori error analysis of a multiscale operator decomposition finite element method for the solution of a system of coupled elliptic problems. The goal is to compute accurate error estimates that account for the effects arising from multiscale discretization via operator decomposition. Our approach to error estimation is(More)
We describe and test an adaptive algorithm for evolution problems that employs a sequence of " blocks " consisting of fixed, though nonuniform, space meshes. This approach offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing, remeshing, matrix reassembly, and the solution of adjoint problems used(More)
SUMMARY In this paper, we develop an a posteriori error analysis for operator decomposition iteration methods applied to systems of coupled semilinear elliptic problems. The goal is to compute accurate error estimates that account for the combined effects arising from numerical approximation (discretization) and operator decomposition iteration. In an(More)
Sensitivity analysis (SA) is a fundamental tool of uncertainty quantification(UQ). Adjoint-based SA is the optimal approach in many large-scale applications, such as the direct numerical simulation (DNS) of combustion. However, one of the challenges of the adjoint workflow for time-dependent applications is the storage and I/O requirements for the(More)
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