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Applied Math Seminar – Lin Mu, Oak Ridge National Laboratory

October 27, 2017 @ 3:30 pm - 4:30 pm

Title: A Priori and a posteriori error estimate for weak Galerkin finite element method on polygonal meshes

Abstract:  Polygonal mesh has advantages including lower DOFs requirement for the same level of accuracy and more flexibility in generating mesh, and better mesh quality over standard discretization with quad mesh or triangular mesh. Also the hanging nodes are handled naturally, which will introduce more simple refinement strategies when applied into the adaptive finite element methods. Furthermore, because the relax of continuity requirement, the numerical schemes for the PDEs solver can be easily extended to high-order schemes by utilizing polynomials with higher degrees. In this talk, we will discuss about the novel weak Galerkin finite element methods to discrete the PDEs and analyze the a priori and a posteriori error estimate accordingly. The key of this new method is to replace the derivatives by their weak discrete derivatives. The new method is a discontinuous finite element approach, which is parameter free, symmetric, and absolutely stable. The fully computable a posteriori error estimate gives an reliable estimate for the interested error. We will also show the robustness of our approach theoretically and numerically.

Details

Date:
October 27, 2017
Time:
3:30 pm - 4:30 pm
Event Categories:
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Venue

228 Gordon Palmer Hall
Tuscaloosa, AL 35487 United States + Google Map