scholarly journals Maximum Principles for $P1$-Conforming Finite Element Approximations of Quasi-linear Second Order Elliptic Equations

2012 ◽  
Vol 50 (2) ◽  
pp. 626-642 ◽  
Author(s):  
Junping Wang ◽  
Ran Zhang
Keyword(s):  
Finite Element ◽  
Elliptic Equations ◽  
Second Order ◽  
Maximum Principles ◽  
Finite Element Approximations ◽  
Conforming Finite Element ◽  
Second Order Elliptic Equations

Discrete maximum principles for nonlinear elliptic finite element problems on surfaces with boundary

2018 ◽  
Vol 40 (2) ◽  
pp. 1241-1265 ◽  
Author(s):  
János Karátson ◽  
Balázs Kovács ◽  
Sergey Korotov
Keyword(s):  
Finite Element ◽  
Maximum Principle ◽  
Elliptic Equations ◽  
Real Life ◽  
Maximum Principles ◽  
The Maximum Principle ◽  
Nonlinear Elliptic ◽  
Discrete Analogues ◽  
Second Order Elliptic Equations ◽  
The Given

AbstractThe maximum principle forms an important qualitative property of second-order elliptic equations; therefore, its discrete analogues, the so-called discrete maximum principles (DMPs), have drawn much attention owing to their role in reinforcing the qualitative reliability of the given numerical scheme. In this paper DMPs are established for nonlinear finite element problems on surfaces with boundary, corresponding to the classical pointwise maximum principles on Riemannian manifolds in the spirit of Pucci & Serrin (2007, The Maximum Principle. Springer). Various real-life examples illustrate the scope of the results.

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