@article{GrajewskiHronTurek2006, author = {Grajewski, Matthias and Hron, Jaroslav and Turek, Stefan}, title = {Numerical analysis for a new non-conforming linear finite element on quadrilaterals}, series = {Journal of Computational and Applied Mathematics}, volume = {193}, journal = {Journal of Computational and Applied Mathematics}, number = {1}, issn = {0377-0427}, doi = {10.1016/j.cam.2005.05.024}, pages = {38 -- 50}, year = {2006}, language = {en} } @article{GrajewskiHronTurek2005, author = {Grajewski, Matthias and Hron, Jaroslav and Turek, Stefan}, title = {Dual weighted a posteriori error estimation for a new nonconforming linear finite element on quadrilaterals}, series = {Applied Numerical Mathematics}, volume = {54}, journal = {Applied Numerical Mathematics}, number = {3-4}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0168-9274}, doi = {10.1016/j.apnum.2004.09.016}, pages = {504 -- 518}, year = {2005}, abstract = {After a short introduction of a new nonconforming linear finite element on quadrilaterals recently developed by Park, we derive a dual weighted residual-based a posteriori error estimator (in the sense of Becker and Rannacher) for this finite element. By computing a corresponding dual solution we estimate the error with respect to a given target error functional. The reliability and efficiency of this estimator is analyzed in several numerical experiments.}, language = {en} }