scholarly journals Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data

2014 ◽  
Vol 38 (13) ◽  
pp. 2850-2863 ◽  
Author(s):  
Helmut Harbrecht ◽  
Giannoula Mitrou
Keyword(s):  
Dirichlet Data ◽  
Bernoulli Problem

scholarly journals Finite element algorithms for nonlocal minimal graphs

2021 ◽  
Vol 4 (2) ◽  
pp. 1-29
Author(s):  
Juan Pablo Borthagaray ◽  
◽  
Wenbo Li ◽  
Ricardo H. Nochetto ◽  
◽  
...  
Keyword(s):  
Mean Curvature ◽  
Numerical Experiments ◽  
Piecewise Linear ◽  
Gradient Flow ◽  
Minimal Graphs ◽  
Qualitative And Quantitative ◽  
Dirichlet Data ◽  
Data Truncation ◽  
Discrete Problems ◽  
Newton Scheme

<abstract><p>We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.</p></abstract>

scholarly journals Nonconforming Finite Element Method Applied to the Driven Cavity Problem

2017 ◽  
Vol 21 (4) ◽  
pp. 1012-1038 ◽  
Author(s):  
Roktaek Lim ◽  
Dongwoo Sheen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Nonconforming Finite Element ◽  
Element Space ◽  
Nonconforming Finite Element Method ◽  
Driven Cavity ◽  
Dirichlet Data ◽  
Minimal Modification ◽  
Element Method

AbstractA cheapest stable nonconforming finite element method is presented for solving the incompressible flow in a square cavity without smoothing the corner singularities. The stable cheapest nonconforming finite element pair based on P1×P0 on rectangularmeshes [29] is employed with a minimal modification of the discontinuous Dirichlet data on the top boundary, where is the finite element space of piecewise constant pressures with the globally one-dimensional checker-board pattern subspace eliminated. The proposed Stokes elements have the least number of degrees of freedom compared to those of known stable Stokes elements. Three accuracy indications for our elements are analyzed and numerically verified. Also, various numerous computational results obtained by using our proposed element show excellent accuracy.

The Bernoulli Problem

1987 ◽  
pp. 5-33 ◽  
Author(s):  
Sergei M. Rytov ◽  
Yurii A. Kravtsov ◽  
Valeryan I. Tatarskii
Keyword(s):  
Bernoulli Problem

scholarly journals A Dirichlet–Neumann cost functional approach for the Bernoulli problem

2013 ◽  
Vol 81 (1) ◽  
pp. 157-176 ◽  
Author(s):  
A. Ben Abda ◽  
F. Bouchon ◽  
G. H. Peichl ◽  
M. Sayeh ◽  
R. Touzani
Keyword(s):  
Functional Approach ◽  
Cost Functional ◽  
Bernoulli Problem
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