Numerical Simulation of Two-Dimensional Pucci’s Equation with Dirichlet Boundary Conditions Using Nonvariational Finite Element Method

2018 ◽  
Author(s):  
Garima Mishra ◽  
Manoj Kumar
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Element Method

APPROXIMATE AND LOW REGULARITY DIRICHLET BOUNDARY CONDITIONS IN THE GENERALIZED FINITE ELEMENT METHOD

2007 ◽  
Vol 17 (12) ◽  
pp. 2115-2142 ◽  
Author(s):  
IVO BABUŠKA ◽  
VICTOR NISTOR ◽  
NICOLAE TARFULEA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Generalized Finite Element Method ◽  
Low Regularity ◽  
Generalized Finite Element ◽  
Element Method

We propose a method for treating Dirichlet boundary conditions for the Laplacian in the framework of the Generalized Finite Element Method (GFEM). A particular interest is taken in boundary data with low regularity (possibly a distribution). Our method is based on using approximate Dirichlet boundary conditions and polynomial approximations of the boundary. The sequence of GFEM-spaces consists of nonzero boundary value functions, and hence it does not conform to one of the basic Finite Element Method (FEM) conditions. We obtain quasi-optimal rates of convergence for the sequence of GFEM approximations of the exact solution. We also extend our results to the inhomogeneous Dirichlet boundary value problem, including the case when the boundary data has low regularity (i.e. is a distribution). Finally, we indicate an effective technique for constructing sequences of GFEM-spaces satisfying our assumptions by using polynomial approximations of the boundary.

LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS

2013 ◽  
Vol 23 (05) ◽  
pp. 777-801 ◽  
Author(s):  
BENQI GUO ◽  
LIJUN YI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Three Dimensions ◽  
The Finite Element Method ◽  
Hexahedral Elements ◽  
Interpolation Operators ◽  
Element Method

In this paper, we construct local Chebyshev projection–interpolation operators for tetrahedral and hexahedral elements in three dimensions based on the framework of the Jacobi-weighted Sobolev and Besov spaces. A simple assembly of the local Chebyshev projection–interpolations ΠΩj u on all the elements Ωj, 1 ≤ j ≤ J, leads to a globally continuous and piecewise polynomial which possesses the best approximation properties locally and globally. By applying the local Chebyshev projection–interpolation operators to the h–p version of the finite element method with general tetrahedral or hexahedral meshes for second-order elliptic problems in three dimensions, we establish the convergence rate for problems with homogeneous Dirichlet boundary conditions and the solution [Formula: see text], and for problems with nonhomogeneous Dirichlet boundary conditions and the solution [Formula: see text].

scholarly journals HEAT TRANSFER IN MULTI-CONNECTED AND IRREGULAR DOMAINS WITH NON-UNIFORM MESHES

2008 ◽  
Vol 7 (2) ◽  
pp. 44
Author(s):  
E. C. Romão ◽  
J. B. Aparecido ◽  
J. B. Campos-Silva ◽  
L. F. M. Moura
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Connected Domain ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
The Finite Element Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Dimensional Diffusion ◽  
Element Method

In this work is presented a numerical solution for temperature profile in two-dimensional diffusion inside irregular multi-connected geometry. The special discretization has been done by two variants of the finite Element Method: Galerkin Finite Element Method (GFEM) and Least Squares Finite Element Method (LSFEM). Three applications are presented. The first for a regular double connected domain; the second for a regular multi-connected domain and the third application for an irregular multi-connected domain. In all applications are considered Dirichlet boundary conditions. The results obtained in the present work are compared with results from Ansys® simulations. The results of each method are presented and discussed and the characteristics and advantages of the methods are also discussed.

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