A uniform high-order method for a singular perturbation problem in conservative form

1992 ◽  
Vol 13 (10) ◽  
pp. 909-916
Author(s):  
Wu Qi-guang ◽  
Sun Xiao-di
Keyword(s):  
Singular Perturbation ◽  
High Order ◽  
Singular Perturbation Problem ◽  
Order Method ◽  
High Order Method ◽  
Perturbation Problem ◽  
Conservative Form

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
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