MooAFEM: An object oriented Matlab code for higher-order adaptive FEM for (nonlinear) elliptic PDEs

Innerberger, Michael; Praetorius, Dirk

doi:10.48550/arxiv.2203.01845

Cited by 2 publications

(2 citation statements)

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“…The number of samples is adjusted to balance statistical error and discretization bias on each level. The experiment has been implemented in MATLAB using the MooAFEM library [11] for the FE discretization. All arising linear systems are solved directly by the \-operator in MATLAB.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure

Longo¹,

Schwab²,

Stein³

2023

Preprint

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We propose a novel a-posteriori error estimation technique where the target quantities of interest are ratios of high-dimensional integrals, as occur e.g. in PDE constrained Bayesian inversion and PDE constrained optimal control subject to an entropic risk measure. We consider in particular parametric, elliptic PDEs with affine-parametric diffusion coefficient, on high-dimensional parameter spaces. We combine our recent a-posteriori Quasi-Monte Carlo (QMC) error analysis, with Finite Element a-posteriori error estimation. The proposed approach yields a computable a-posteriori estimator which is reliable, up to higher order terms. The estimator's reliability is uniform with respect to the PDE discretization, and robust with respect to the parametric dimension of the uncertain PDE input.

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Section: Numerical Experimentsmentioning

confidence: 99%

A-posteriori QMC-FEM error estimation for Bayesian inversion and optimal control with entropic risk measure

Longo¹,

Schwab²,

Stein³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In this section, we test and illustrate Algorithm B with numerical experiments. All experiments were implemented using the Matlab code MooAFEM [IP22]. Throughout, Ω ⊂ R 2 and we use x = (x 1 , x 2 ) ∈ Ω to denote the Cartesian coordinates.…”

Section: Numerical Experimentsmentioning

confidence: 99%