Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Prof. Junping Wang, National Science Foundation, USA
Primal-Dual Weak Galerkin Finite Element Methods
Time & Venue:
2019.10.31 10:00-11:00 N602
The weak Galerkin (WG) finite element method is a generic numerical method for partial differential equations. The essence of WG is to reconstruct differential operators in the usual variational forms for partial differential equations (PDE) through a framework that mimics the theory of distributions for piecewise polynomials. The regularity requirements (such as H^1, H^2, H(div), or H(curl) etc) for the underlying approximating functions are compensated by some carefully-designed stabilizers. This framework produces discrete weak differential operators (e.g., weak gradients, weak curl, weak Laplacian etc) which are employed for PDE discretization. The computation of the discrete differential operators involves the solution of inexpensive problems defined locally on each element. Due to the structural flexibility, the WG finite element method is well suited to most PDEs by providing the needed stability and accuracy in mathematics. The resulting numerical scheme often conserves the important physical quantities such as mass and/or energy that the system models. In this talk, the speaker will discuss a primal-dual framework in the weak Galerkin context (PD-WG) for some model PDE problems for which the usual numerical methods are difficult to apply. The speaker will first demonstrate the basic ideas of PD-WG by using a linear transport problem, and will then apply the method to other PDEs including nonlinear PDEs and the div-curl systems with tangential or normal boundary conditions.
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