A posteriori error estimation and adaptive strategy for PGD model reduction applied to parametrized linear parabolic problems
For engineers using PGD model reduction, this work offers certified error control and adaptive refinement, addressing a key bottleneck in reliability.
The paper develops an a posteriori error estimation method for PGD model reduction in parametrized linear parabolic problems, providing guaranteed error bounds and a greedy adaptive strategy. Numerical tests on multi-parameter mechanical problems demonstrate the effectiveness of the approach.
We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it provides guaranteed and fully computable global/goal-oriented error estimates taking both discretization and PGD truncation errors into account. Splitting the error sources, it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of PGD approximations. The focus of the paper is on two technical points: (i) construction of equilibrated fields required to compute guaranteed error bounds; (ii) error splitting and adaptive process when performing PGD-based model reduction. Performances of the proposed verification and adaptation tools are shown on several multi-parameter mechanical problems.