Petrov-Galerkin
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers
Announce Type: replace Abstract: A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used as test functions in one coordinate direction and are combined with bilinear trial functions defined on a Shishkin mesh.
Hessian-recovery-based C0 finite element methods for non-divergence form elliptic equations
arXiv:2606.03276v1 Announce Type: new Abstract: A Hessian-recovery-based C0 finite element framework is proposed for second-order elliptic equations in non-divergence form. The construction is based on a direct approximation of the strong non-divergence operator: the Hessian D2u is replaced by a recovered Hessian Hhuh, so that A : D2u is approximated by A : Hhuh. The resulting discretizations include a nodal formulation and a Galerkin-type formulation for general Lagrange finite element...
$\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation
Announce Type: replace Abstract: This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output $\mathcal{H}_2$ minimization problem.
$H_2$ optimal model reduction of linear systems with multiple quadratic outputs
Announce Type: replace Abstract: In this work, we consider the $H_2$ optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared $H_2$ system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the $H_2$ optimal approximation...