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Bilayer plates are compound materials that exhibit large bending deformations when exposed to environmental changes that lead to different mechanical responses in the involved materials. In this article a new numerical method which is…

Numerical Analysis · Mathematics 2020-04-02 Sören Bartels , Christian Palus

A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the…

Numerical Analysis · Mathematics 2007-05-23 L. Beirao da Veiga , J. Niiranen , R. Stenberg

We introduce a Nitsche's method for the numerical approximation of the Kirchhoff-Love plate equation under general Robin-type boundary conditions. We analyze the method by presenting a priori and a posteriori error estimates in…

Numerical Analysis · Mathematics 2020-07-02 Tom Gustafsson , Rolf Stenberg , Juha Videman

In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic plates as the thickness tends to zero. We choose Terzaghi's time corresponding to the plate thickness and obtain the strong…

Analysis of PDEs · Mathematics 2014-10-23 Anna Marciniak-Czochra , Andro Mikelic

A plate is rigid if its admissible displacement fields inducing vanishing two-dimensional strain tensors must vanish. We prove that the nonlinear model of Kirchhoff-Love for such a plate has a solution for any applied forces and boundary…

Analysis of PDEs · Mathematics 2025-11-19 Trung Hieu Giang , Cristinel Mardare

We propose an alternative approach called backward transformation for the design of platonic cloaks, without resorting to in-plane body forces and pre-stresses, which can lead to unphysical features. It is shown that the Kirchhoff-Love…

Computational Physics · Physics 2019-01-03 Lucas Pomot , Stephane Bourgeois , Cedric Payan , Marcel Remillieux , Sebastien Guenneau

We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces.…

Numerical Analysis · Mathematics 2017-06-06 Erik Burman , Peter Hansbo , Mats G. Larson

Nitsche's method is a well-established approach for weak enforcement of boundary conditions for partial differential equations (PDEs). It has many desirable properties, including the preservation of variational consistency and the fact that…

Numerical Analysis · Mathematics 2022-03-08 Joseph Benzaken , John A. Evans , Rasmus Tamstorf

We address the direct scattering problem for a penetrable obstacle in an infinite elastic two--dimensional Kirchhoff--Love plate. Under the assumption that the plate's thickness is small relative to the wavelength of the incident wave, the…

Analysis of PDEs · Mathematics 2026-02-20 Rafael Ceja Ayala , Isaac Harris , Tonatiuh Sánchez-Vizuet

In this article, we study the semi discrete and fully discrete formulations for a Kirchhoff type quasilinear integro-differential equation involving time-fractional derivative of order $\alpha \in (0,1) $. For the semi discrete formulation…

Numerical Analysis · Mathematics 2023-05-08 Lalit Kumar , Sivaji Ganesh Sista , Konijeti Sreenadh

This work focuses on the development of a posteriori error estimates for fourth-order, elliptic, partial differential equations. In particular, we propose a novel algorithm to steer an adaptive simulation in the context of Kirchhoff plates…

Numerical Analysis · Mathematics 2020-04-22 Pablo Antolin , Annalisa Buffa , Luca Coradello

We consider DPG methods with optimal test functions and broken test spaces based on ultra-weak formulations of general second order elliptic problems. Under some assumptions on the regularity of solutions of the model problem and its…

Numerical Analysis · Mathematics 2017-12-22 Thomas Führer

This work presents a new hybrid discretization approach to alleviate membrane locking in isogeometric finite element formulations for Kirchhoff-Love shells. The approach is simple, and requires no additional dofs and no static condensation.…

Computational Engineering, Finance, and Science · Computer Science 2025-09-09 Roger A. Sauer , Zhihui Zou , Thomas J. R. Hughes

We propose and analyze a discretization scheme that combines the discontinuous Petrov-Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition…

Numerical Analysis · Mathematics 2017-04-26 Thomas Führer , Norbert Heuer , Michael Karkulik , Rodolfo Rodríguez

Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…

Numerical Analysis · Mathematics 2016-08-16 Robert Eymard , Thierry Gallouët , Raphaèle Herbin

We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based on each pair, we design a discretization that is…

Numerical Analysis · Mathematics 2019-02-12 Christian Kreuzer , Pietro Zanotti

We develop a discontinuous Petrov-Galerkin scheme with optimal test functions (DPG method) for the Timoshenko beam bending model with various boundary conditions, combining clamped, supported, and free ends. Our scheme approximates the…

Numerical Analysis · Mathematics 2020-04-02 Thomas Führer , Carlos García Vera , Norbert Heuer

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner…

Computational Engineering, Finance, and Science · Computer Science 2019-05-08 Christoph Meier , Wolfgang A. Wall , Alexander Popp

We perform a dimension reduction analysis for a coupled rate-dependent/rate-independent adhesive-contact model in the setting of visco-elastodynamic plates. We work with a weak solvability notion inspired by the theory of (purely)…

Analysis of PDEs · Mathematics 2025-11-14 Giovanna Bonfanti , Elisa Davoli , Riccarda Rossi

We prove a version of faithfully flat descent in rigid analytic geometry, for almost perfect complexes and without finiteness assumptions on the rings involved. This extends results of Drinfeld for vector bundles.

Algebraic Geometry · Mathematics 2021-09-14 Akhil Mathew