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8 papers · 1 filter
A posteriori error estimators for hierarchical B-spline discretizations
Annalisa Buffa, Eduardo M. Garau
In this article we develop function-based a posteriori error estimators for the solution of linear second order elliptic problems considering hierarchical spline spaces for the Gal…
PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spaces
A. F. Sarmiento, A. M. A. Cortes, D. A. Garcia +3
We describe the development of a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, PetIGA-MF i…
Generalized Qualification and Qualification Levels for Spectral Regularization Methods
Terry Herdman, Ruben D. Spies, Karina G. Temperini
The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization err…
On convex functions and the finite element method
Néstor Aguilera, Pedro Morin
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex f…
Approximating optimization problems over convex functions
Néstor E. Aguilera, Pedro Morin
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H…
Convergence rates for adaptive finite elements
Fernando D. Gaspoz, Pedro Morin
In this article we prove that it is possible to construct, using newest-vertex bisection, meshes that equidistribute the error in -norm, whenever the function to approximate c…