Additive Schwarz Methods for the hp-Version

2021 ◽  
pp. 127-141
Author(s):  
Ernst P. Stephan ◽  
Thanh Tran
Keyword(s):  
Schwarz Methods ◽  
Additive Schwarz ◽  
Additive Schwarz Methods

scholarly journals A BDDC Preconditioner for the RotatedQ1FEM for Elliptic Problems with Discontinuous Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yaqin Jiang
Keyword(s):  
Finite Element Method ◽  
Elliptic Equations ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Discontinuous Coefficients ◽  
Schwarz Methods ◽  
Additive Schwarz ◽  
Variational Form ◽  
Second Order Elliptic Equations ◽  
Additive Schwarz Methods

We propose a BDDC preconditioner for the rotatedQ1finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.

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