scholarly journals A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions

2004 ◽  
Vol 74 (251) ◽  
pp. 1217-1231 ◽  
Author(s):  
Adam M. Oberman
Keyword(s):  
Difference Scheme ◽  
Infinity Laplacian ◽  
Lipschitz Extensions ◽  
Convergent Difference Scheme

An Unconditionally Stable and High-Order Convergent Difference Scheme for Stokes’ First Problem for a Heated Generalized Second Grade Fluid with Fractional Derivative

2017 ◽  
Vol 10 (3) ◽  
pp. 597-613 ◽  
Author(s):  
Cuicui Ji ◽  
Zhizhong Sun
Keyword(s):  
Fractional Derivative ◽  
Difference Scheme ◽  
Second Order ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Unconditionally Stable ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Second Order Convergence ◽  
Convergent Difference Scheme

AbstractThis article is intended to fill in the blank of the numerical schemes with second-order convergence accuracy in time for nonlinear Stokes’ first problem for a heated generalized second grade fluid with fractional derivative. A linearized difference scheme is proposed. The time fractional-order derivative is discretized by second-order shifted and weighted Gr¨unwald-Letnikov difference operator. The convergence accuracy in space is improved by performing the average operator. The presented numerical method is unconditionally stable with the global convergence order of in maximum norm, where τ and h are the step sizes in time and space, respectively. Finally, numerical examples are carried out to verify the theoretical results, showing that our scheme is efficient indeed.

scholarly journals Optimal Lipschitz extensions and the infinity laplacian

2001 ◽  
Vol 13 (2) ◽  
pp. 123-139 ◽  
Author(s):  
M.G. Crandall ◽  
L.C. Evans ◽  
R.F. Gariepy
Keyword(s):  
Infinity Laplacian ◽  
Lipschitz Extensions
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