HIGH ORDER METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATIONS WITH SMALL SHIFTS

2013 ◽  
Vol 88 (2) ◽  
Author(s):  
A.A. Salama ◽  
D.G. Al-Amery
Keyword(s):  
Difference Equations ◽  
High Order ◽  
Singularly Perturbed ◽  
Order Method ◽  
High Order Method

scholarly journals Hybrid high-order method for singularly perturbed fourth-order problems on curved domains

2021 ◽  
Author(s):  
Zhaonan Dong ◽  
Alexandre Ern
Keyword(s):  
Singular Perturbation ◽  
Fourth Order ◽  
Mesh Size ◽  
Perturbation Parameter ◽  
High Order ◽  
Singularly Perturbed ◽  
Optimal Error Estimates ◽  
Order Method ◽  
High Order Method ◽  
Type Boundary

We propose a novel hybrid high-order method (HHO) to approximate singularly perturbed fourth-order PDEs on domains with a possibly curved boundary. The two key ideas in devising the method are the use of a Nitsche-type boundary penalty technique to weakly enforce the boundary conditions and a scaling of the weighting parameter in the stabilisation operator that compares the singular perturbation parameter to the square of the local mesh size. With these ideas in hand, we derive stability and optimal error estimates over the whole range of values for the singular perturbation parameter, including the zero value for which a second-order elliptic problem is recovered. Numerical experiments illustrate the theoretical analysis.

Theoretical Aspects of a Multidomain High-Order Method for CAA

2003 ◽  
Author(s):  
Ronan Guenanff ◽  
Pierre Sagaut ◽  
Eric Manoha ◽  
Marc Terracol ◽  
Roger Lewandowsky
Keyword(s):  
High Order ◽  
Order Method ◽  
High Order Method

Analysis of a filtered high-order method for CAA

2003 ◽  
pp. 1978-1981 ◽  
Author(s):  
R. Guénanff ◽  
P. Sagaut ◽  
E. Manoha ◽  
R. Lewandowski
Keyword(s):  
High Order ◽  
Order Method ◽  
High Order Method
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