Convergence analysis of an hp finite element method for singularly perturbed transmission problems in smooth domains

2013 ◽  
Vol 29 (6) ◽  
pp. 2107-2132
Author(s):  
Serge Nicaise ◽  
Christos Xenophontos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Convergence Analysis ◽  
Singularly Perturbed ◽  
Transmission Problems ◽  
Element Method ◽  
Hp Finite Element

THE hp FINITE ELEMENT METHOD FOR SINGULARLY PERTURBED PROBLEMS IN SMOOTH DOMAINS

1998 ◽  
Vol 08 (02) ◽  
pp. 299-326 ◽  
Author(s):  
CHRISTOS A. XENOPHONTOS
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Approximation ◽  
Singularly Perturbed ◽  
Exponential Rate ◽  
Product Spaces ◽  
Singularly Perturbed Problems ◽  
Smooth Part ◽  
Element Method ◽  
Hp Finite Element

We consider the numerical approximation of singularly perturbed elliptic problems in smooth domains. The solution to such problems can be decomposed into a smooth part and a boundary layer part. We present guidelines for the effective resolution of boundary layers in the context of the hp finite element method and we construct tensor product spaces that approximate these layers uniformly at a near-exponential rate.

An hp finite element method for 4th order singularly perturbed problems

2016 ◽  
Vol 73 (2) ◽  
pp. 567-590 ◽  
Author(s):  
Philippos Constantinou ◽  
Charalambia Varnava ◽  
Christos Xenophontos
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
Element Method ◽  
Hp Finite Element
Sign in / Sign up

Export Citation Format

Share Document