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Numerical Approximation of a PDE‐Constrained Optimization Problem that Appears in Data‐Driven Computational Mechanics

International Journal for Numerical Methods in Engineering, Volume 127, Issue 4, 28 February 2026.
ABSTRACT We investigate an optimization problem that arises when working within the paradigm of Data‐Driven Computational Mechanics. In the context of the diffusion‐reaction problem, such an optimization problem seeks the continuous primal fields (gradient and flux) that are closest to some predefined discrete fields taken from a material data set. The
Pedro B. Bazon +3 more
wiley +1 more source

A Compact Difference-Galerkin Spectral Method of the Fourth-Order Equation with a Time-Fractional Derivative

Fractal and Fractional
In this article, we proposed a compact difference-Galerkin spectral method for the fourth-order equation in multi-dimensional space with the time-fractional derivative order α∈(1,2).
Yujie Wang, Shichao Yi
doaj +1 more source

Distributional derivatives and stability of discontinuous Galerkin finite element approximation methods

Electronic Journal of Differential Equations, 2016
The goal of this article is to explore and motivate stabilization requirements for various types of discontinuous Galerkin (DG) methods. A new approach for the understanding of DG approximation methods for second order elliptic partial differential ...
Thomas Lewis
doaj

The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems

, 1998
Bernardo Cockburn, Chi-Wang Shu
semanticscholar +1 more source

TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework

, 1989
Bernardo Cockburn, Chi-Wang Shu
semanticscholar +1 more source

Analytical study of mode filtering in a duct with resistive layers. [PDF]

PLoS One
Alahmadi H, Afzal M, Javeed U, Nawaz T.
europepmc +1 more source

Inf-sup stable space-time Local Discontinuous Galerkin method for the heat equation. [PDF]

J Sci Comput
Gómez S, Perinati C, Stocker P.
europepmc +1 more source

hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes

, 2017
A. Cangiani, E. Georgoulis, P. Houston
semanticscholar +1 more source

Positivity-Preserving Hybridizable Discontinuous Galerkin Scheme for Solving PNP Model. [PDF]

Entropy (Basel)
Morales D, Xu Z.
europepmc +1 more source