2025/02/20 by Yohance A. P. Osborne, Osborne, Yohance A. P., Iain Smears +3 · 1 citation
Engineering · Mathematics · Decision Sciences · #Advanced Numerical Methods in Computational Mathematics #Numerical methods for differential equations #Probabilistic and Robust Engineering Design
paper · doi:10.48550/arxiv.2502.14687
We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the H1-norm of the error and the dual norm of the residual. We then derive reliable and efficient estimators for a broad class of stabilized first-order finite element methods. We also show that in the case of affine-preserving stabilizations, the estimator can be further simplified to the standard residual estimator. Numerical experiments illustrate the computational gains in efficiency and accuracy from the estimators in the context of adaptive methods.