order method
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Author(s):  
Zhaonan Dong ◽  
Alexandre Ern

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.


2021 ◽  
pp. 161-174
Author(s):  
Ioannis K. Argyros

Author(s):  
Zhengwen Tu ◽  
Liangwei Wang ◽  
Yongxiang Zhao ◽  
Tao Peng ◽  
Xinsong Yang ◽  
...  

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