Title: Non-conforming Least-squares Spectral Element Method for Stokes Equations
Speaker: Dr Subhashree Mohapatra (IIT Bhubaneswar)
Time: 3:30 to 4:30pm, Thursday, January 9, 2014
Venue: TBA
Abstract: In the first part we propose a non-conforming hp spectral element method to solve two dimensional Stokes equations with primitive variable formulation on distributed memory based parallel computers. The method is essentially a least-squares method and applicable to both smooth and non-smooth domains. We use geometrical meshes near the corners to overcome the singularities. The transformation \(P^k=e^{τ_k} p\) is used along the sectoral region to resolve the singularity of pressure variable. A suitable parallelizable block diagonal preconditioner is constructed so that the condition number of the preconditioned system is \(O((\ln W)^2)\), where W is the degree of polynomial.
We prove our method to be exponentially accurate. Preconditioned conjugate gradient method is used to obtain the numerical solution. The method is applicable to Dirichlet, Neumann, mixed boundary conditions. Finally we present numerical results on smooth and non-smooth domains with different boundary conditions and discuss computational complexity of the method.
In the second part of the work a three dimensional Stokes problem on smooth domains with Dirichlet boundary conditions is discussed. Numerical results on a cube are presented.
