Monotonicity recovering and accuracy preserving optimization methods for postprocessing finite element solutions

• We suggest here a least-change correction to available finite element (FE) solution.This postprocessing procedure is aimed at recoveringthe monotonicity and some other important properties that may not beexhibited by the FE solution. It is based on solvinga monotonic regression problem with some extra constraints.One of them is a linear equality-type constraint which models the conservativityrequirement. The other ones are box-type constraints, andthey originate from the discrete maximum principle.The resulting postprocessing problem is a large scale quadratic optimization problem. It is proved that the postprocessedFE solution preserves the accuracy of the discrete FE approximation.We introduce an algorithm for solving the postprocessingproblem. It can be viewed as a dual ascent method basedon the Lagrangian relaxation of the equality constraint.We justify theoretically its correctness.Its efficiency is demonstrated by the presented results of numerical experiments.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Constrained monotonic regression

Large scale quadratic optimization

Lagrangian relaxation

Dual ascent method

Finite element solution

Accuracy analysis

Optimization, systems theory

Optimeringslära, systemteori

Numerical analysis

Numerisk analys

Publikations- och innehållstyp

vet (ämneskategori)

rap (ämneskategori)