TY - GEN A1 - Carstensen, Carsten A1 - Peterseim, Daniel A1 - Schedensack, Mira T1 - Comparison Results of Three First-order Finite Element Methods for the Poisson Model Problem N2 - This paper establishes the equivalence of conforming Courant finite element method and nonconforming Crouzeix-Raviart finite element method in the sense that the respective energy error norms are equivalent up to generic constants and higher-order data oscillations in a Poisson model problem. The Raviart-Thomas mixed finite element method is better than the previous two whereas the conjecture of the converse relation is proved to be false. This paper completes the analysis of comparison initiated by Braess in Calcolo (2010). Two numerical benchmarks illustrate the comparison theorems and the possible strict superiority of the Raviart-Thomas mixed finite element method. Applications include least-squares finite element methods and equality of approximation classes for concepts of optimality for adaptive finite element methods. KW - finite element method KW - nonconforming FEM KW - Crouzeix-Raviart KW - Raviart-Thomas KW - least-squares method KW - approximation class Y1 - 2011 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/940 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-9407 ER -