scholarly journals A finite element method for a diffusion equation with constrained energy and nonlinear boundary conditions

1993 ◽  
Vol 35 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Amiya K. Pani
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Diffusion Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nonlinear Boundary Conditions ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Finite Element Galerkin Method

AbstractA finite element Galerkin method for a diffusion equation with constrained energy and nonlinear boundary condition is analysed and optimal error estimates in L2 and L∞-norms are derived. These results improve upon previously derived estimates by Cannon et al. [4].

Bounds for blow-up time for the heat equation under nonlinear boundary conditions

2009 ◽  
Vol 139 (6) ◽  
pp. 1289-1296 ◽  
Author(s):  
L. E. Payne ◽  
P. W. Schaefer
Keyword(s):  
Boundary Condition ◽  
Lower Bound ◽  
Heat Equation ◽  
Differential Inequality ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Sufficient Condition ◽  
Inequality Technique

A differential inequality technique is used to determine a lower bound on the blow-up time for solutions to the heat equation subject to a nonlinear boundary condition when blow-up of the solution does occur. In addition, a sufficient condition which implies that blow-up does occur is determined.

scholarly journals A Consistent Immersed Finite Element Method for the Interface Elasticity Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Sangwon Jin ◽  
Do Y. Kwak ◽  
Daehyeon Kyeong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rates Of Convergence ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Immersed Finite Element Method ◽  
Elasticity Problems ◽  
Interface Elasticity ◽  
Nonconforming Finite Element Methods ◽  
Element Method

We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on theP1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates inH1and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence.

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