Computational Math Seminar: Steffen Münzenmaier
A Comparison of Finite Element Spaces for H(div) Conforming First-Order System Least Squares
Steffen Münzenmaier
Applied Mathematics,Ìý
Date and time:Ìý
Tuesday, October 20, 2015 - 11:00am
³¢´Ç³¦²¹³Ù¾±´Ç²Ô:Ìý
GRVW 105
´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý
First-order system least squares (FOSLS) is a commonly used technique in a wide range of physical applications. FOSLS discretizations are straightforward to implement and offer many advantages over traditional Galerkin or saddle point formulations. Often these problems are formulated in H(div) spaces and H(div)-conforming elements are used. These elements have lesser regularity assumptions than the commonly used H1-conforming elements and are therefore believed to be more suited for singular problems arising in many applications. After introducing the least squares finite element method and the finite element spaces, this talk will compare the approximation properties of the H(div)-conforming Raviart-Thomas and Brezzi-Douglas-Marini elements to H1-conforming piecewise polynomials in a H(div)-setting. Furthermore a H1-formulation for these problems will be derived and compared to the H(div)-formulation. For the comparison typical Poisson/Stokes problems are examined and singular solutions will be addressed byÌý adaptive refinement strategies.