A posteriori error bounds for finite element approximations of steady-state mean field games

Abstract

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 $H^1$-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.

References in corpus (4)

• Analysis and Numerical Approximation of Stationary Second-Order Mean Field Game Partial Differential Inclusions
• Finite element approximation of time-dependent mean field games with nondifferentiable Hamiltonians
• Near and full quasi-optimality of finite element approximations of stationary second-order mean field games
• Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions

Cited by in corpus (1)

• Rates of convergence of finite element approximations of second-order mean field games with nondifferentiable Hamiltonians