===firstname:
Steffen
===firstname3:
Thomas
===affil6:

===lastname3:
Manteuffel
===email:
steffen.muenzenmaier@colorado.edu
===keyword_other2:

===lastname6:

===affil5:

===lastname4:

===lastname7:

===affil7:

===postal:
1ECOT
Engineering Office Tower
1111 Engineering Drive
Boulder CO 80309
===ABSTRACT:
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 $H^1$-conforming elements and are therefore believed to be more suited for singular problems arising in many applications. This talk will compare the approximation properties of the $H(div)$-conforming Raviart-Thomas and Brezzi-Douglas-Marini elements to $H^1$-conforming piecewise polynomials in a $H(div)$-setting. Furthermore a $H^1$-formulation for these problems will be used and compared to the $H(div)$-formulation. For the comparison typical Poisson/Stokes problems are examined and singular solutions will be addressed by  adaptive refinement strategies. 
===affil3:
University of Colorado Boulder
===title:
A Comparison of Finite Element Spaces for $H(div)$-Conforming First-Order System Least Squares
===affil2:
University of Colorado Boulder
===lastname2:
Leibs
===firstname4:

===keyword1:
APP_OTHER
===workshop:
no
===lastname:
Muenzenmaier
===firstname5:

===keyword2:
NOT_SPECIFIED
===otherauths:

===affil4:

===competition:
no
===firstname7:

===firstname6:

===keyword_other1:
Linear First-Order System Least Squares
===lastname5:

===affilother:

===firstname2:
Christopher