English
Related papers

Related papers: Cut Bogner-Fox-Schmit Elements for Plates

200 papers

We establish the convergence of an adaptive spline-based finite element method of a fourth order elliptic problem with weakly-imposed Dirichlet boundary conditions using polynomial B-splines.

Numerical Analysis · Mathematics 2018-12-21 Ibrahim Al Balushi

The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…

Numerical Analysis · Mathematics 2018-02-20 Simon Sticko , Gunilla Kreiss

The third-order Jeffery-Hamel ODE governing the flow of an incompressible fluid in a two-dimensional wedge is briefly derived, and a C^1 finite element formulation of the equation is developed. This formulation has several advantages,…

Numerical Analysis · Mathematics 2016-12-20 John W. Peterson , Roy H. Stogner

We develop two unfitted finite element methods for the Stokes equations using $H^{\text{div}}$-conforming finite elements. Both methods achieve optimal convergence for velocity, ensure pointwise divergence-free velocity fields, and produce…

Numerical Analysis · Mathematics 2024-09-04 Thomas Frachon , Erik Nilsson , Sara Zahedi

We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…

Numerical Analysis · Mathematics 2018-01-03 Peter Hansbo , Tobias Jonsson , Mats G. Larson , Karl Larsson

The performance of a Cosserat/micropolar solid as a numerical vehicle to represent dispersive media is explored. The study is conducted using the finite element method with emphasis on Hermiticity, positive definiteness, principle of…

Computational Physics · Physics 2019-09-17 Nicolás Guarín-Zapata , Juan Gomez , Camilo Valencia , Gary F. Dargush , Ali Reza Hadjesfandiari

We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite…

Numerical Analysis · Mathematics 2013-05-13 Bishnu P. Lamichhane

A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based…

Computational Engineering, Finance, and Science · Computer Science 2020-07-02 Michael Gfrerer

We propose a Nitsche-based fictitious domain method for the three field Stokes problem in which the boundary of the domain is allowed to cross through the elements of a fixed background mesh. The dependent variables of velocity, pressure…

Numerical Analysis · Mathematics 2015-02-23 Erik Burman , Susanne Claus , André Massing

We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries.…

Numerical Analysis · Mathematics 2023-09-06 Nabil M. Atallah , Vladimir Z. Tomov , Guglielmo Scovazzi

We present a method of CutFEM type for the Poisson problem with either Dirichlet or Neumann boundary conditions. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements…

Numerical Analysis · Mathematics 2019-09-04 Alexei Lozinski

In this note we design a cut finite element method for a low order divergence free element applied to a boundary value problem subject to Stokes' equations. For the imposition of Dirichlet boundary conditions we consider either Nitsche's…

Numerical Analysis · Mathematics 2023-11-14 Erik Burman , Peter Hansbo , Mats G. Larson

We introduce bivariate $C^1$ piecewise quintic finite element spaces for curved domains enclosed by piecewise conics satisfying homogeneous boundary conditions, construct local bases for them using Bernstein-B\'ezier techniques, and…

Numerical Analysis · Mathematics 2025-08-26 Oleg Davydov , Abid Saeed

We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…

Numerical Analysis · Mathematics 2021-01-26 Erik Burman , Peter Hansbo , Mats G. Larson

We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…

Numerical Analysis · Mathematics 2016-02-18 Oleg Davydov , Georgii Kostin , Abid Saeed

A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element,…

Numerical Analysis · Mathematics 2018-10-23 Javier Videla , Sundararajan Natarajan , Stephane PA Bordas

This paper presents the Finite Element Method for Cosserat plates. The mathematical model for Cosserat elastic plates is based on the calculation of the optimal value of the splitting parameter. We discuss the existence and uniqueness of…

Numerical Analysis · Mathematics 2016-02-26 Roman Kvasov , Lev Steinberg

In the article the formulas for the modeling of conservative fields in piecewise infinite plate with a thin inclusion found. The accuracy of the found formulas is of order equal to the thickness of the outer layer. The problem for higher…

Analysis of PDEs · Mathematics 2013-09-27 O. Yaremko , E. Mogileva

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

We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…

Numerical Analysis · Mathematics 2025-03-12 José Joaquín Carvajal , Davood Damircheli , Thomas Führer , Francisco Fuica , Michael Karkulik