A nonlinear problem with Signorini boundary conditions and non regular data

2018 ◽  
Author(s):  
Lucio Boccardo ◽  
G. Rita Cirmi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Signorini Boundary Conditions

scholarly journals Hybrid high-order discretizations combined with Nitsche’s method for Dirichlet and Signorini boundary conditions

2020 ◽  
Vol 40 (4) ◽  
pp. 2189-2226 ◽  
Author(s):  
Karol L Cascavita ◽  
Franz Chouly ◽  
Alexandre Ern
Keyword(s):  
Boundary Conditions ◽  
Error Estimates ◽  
High Order ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Nitsche’S Method ◽  
Nitsche's Method ◽  
Elliptic Model ◽  
The Face ◽  
Signorini Boundary Conditions

Abstract We present two primal methods to weakly discretize (linear) Dirichlet and (nonlinear) Signorini boundary conditions in elliptic model problems. Both methods support polyhedral meshes with nonmatching interfaces and are based on a combination of the hybrid high-order (HHO) method and Nitsche’s method. Since HHO methods involve both cell unknowns and face unknowns, this leads to different formulations of Nitsche’s consistency and penalty terms, either using the trace of the cell unknowns (cell version) or using directly the face unknowns (face version). The face version uses equal-order polynomials for cell and face unknowns, whereas the cell version uses cell unknowns of one order higher than the face unknowns. For Dirichlet conditions, optimal error estimates are established for both versions. For Signorini conditions, optimal error estimates are proven only for the cell version. Numerical experiments confirm the theoretical results and also reveal optimal convergence for the face version applied to Signorini conditions.

Asymptotic Analysis of a Nonlinear Problem on Domain Boundaries in Convection Patterns by Homotopy Renormalization Method

2017 ◽  
Vol 72 (10) ◽  
pp. 909-913 ◽  
Author(s):  
Hua Xin
Keyword(s):  
Asymptotic Analysis ◽  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Variable Coefficient ◽  
Analytic Approximation ◽  
Domain Boundaries ◽  
Convection Patterns ◽  
Renormalization Method ◽  
Homotopy Renormalization Method ◽  
Better Than

AbstractIn this article, using the homotopy renormalization method, the asymptotic analysis to a nonlinear problem on domain boundaries in convection patterns are given. In particular, by taking a variable coefficient homotopy equation, the global asymptotic solutions satisfying boundary conditions are obtained. These results are better than the existing analytic approximation solutions.

scholarly journals Infinitely many solutions for mixed Dirichlet-Neumann problems driven by the (p,q)-laplace operator

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4603-4611 ◽  
Author(s):  
Francesca Vetro
Keyword(s):  
Boundary Conditions ◽  
Laplace Operator ◽  
Nonlinear Problem ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Infinitely Many Solutions ◽  
Neumann Problems ◽  
Reaction Term ◽  
Variational Tools

We study a nonlinear problem with mixed Dirichlet-Neumann boundary conditions involving the p-Laplace operator and the q-Laplace operator ((p,q)-Laplace operator). Using variational tools and appropriate hypotheses on the behavior either at infinity or at zero of the reaction term, we prove that such a problem has infinitely many solutions.

Transient Response in a One-Dimensional Model of Thermoelastic Contact

1996 ◽  
Vol 63 (3) ◽  
pp. 575-581 ◽  
Author(s):  
Z. S. Olesiak ◽  
Yu. A. Pyryev
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Transient Response ◽  
Computational Simulation ◽  
Linear Equations ◽  
Numerical Results ◽  
System Of Equations ◽  
Dimensional Model ◽  
One Dimensional ◽  
Method Of Solution

We consider two layers of different materials with the initial gap between them in the field of temperature with imperfect boundary conditions in Barber’s sense. The model we discuss is that of two contacting rods (Barber and Zhang, 1988) which in the case of a single rod was devised and discussed by Dundurs and Comninou (1976, 1979). In this paper we try to make a step further in the investigation of the essentially nonlinear problem. Though we consider a system of the linear equations of thermoelasticity the nonlinearity is induced by the boundary conditions dependent on the solution. We present an algorithm for solving the system of equations based on Laplace’s transform technique. The method of solution can be used also in the dynamical problems with inertial terms taken into account. The numerical results have been obtained by a kind of computational simulation.

scholarly journals Multiple solutions for p-Laplacian eigenproblem with nonlinear boundary conditions

2016 ◽  
Vol 34 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Mohammed Berrajaa ◽  
Omar Chakrone ◽  
Fatiha Diyer ◽  
Okacha Diyer
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Minimization Method ◽  
The First Eigenvalue

In this paper we study the existence of at least two nontrivial solutions for the nonlinear problem p-Laplacian, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediary eigenvalue problem by the minimization method. In fact, in some sense, we establish the non-resonance below the first eigenvalues of nonlinear Steklov-Robin.

scholarly journals NON-PARALLEL PLANE RAYLEIGH BENARD CONVECTION IN CYLINDRICAL GEOMETRY

1992 ◽  
Vol 23 (3) ◽  
pp. 171-185
Author(s):  
A. GOLBABAI (SHAYGAN)
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Amplitude Equation ◽  
Polar Coordinates ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Problem ◽  
Cylindrical Polar Coordinates ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid sur­ face is of the form $z =\varepsilon^2 g (s)$, in axisymmetric cylindrical polar coordinates, $(r,\phi, z)$. The boundary conditions at $s =0$ for the linear amplitude equation is found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Stewartson (1978) [2], representing a distribution of convection cells near the centre.

On a nonlinear problem with Dirichlet and Acoustic boundary conditions

2021 ◽  
Vol 411 ◽  
pp. 126514
Author(s):  
Adriano A. Alcântara ◽  
Bruno A. Carmo ◽  
Haroldo R. Clark ◽  
Ronald R. Guardia ◽  
Mauro A. Rincon
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Problem ◽  
Acoustic Boundary Conditions
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