ERROR REDUCTION IN ADAPTIVE FINITE ELEMENT APPROXIMATIONS OF ELLIPTIC OBSTACLE PROBLEMS

An educational tool in the form of a word game is disclosed. Each player starts on his own colored starting point at the bottom of the game area. Each player is represented by a colored alphabet set of blocks that are selected before the start of the game. During successive turns, the players must travel up and across the board by forming words while using one letter from the previous word, and must return the remaining letters to a return section of a tray with the letters facing down. All the letters used by a player from his selector holder to form a word must be substituted by the letters from a surplus section of a supply tray. To accomplish their goal and win the game, the players must enter their respective color goal or finish point on the top of the game area. If in a turn more than one player reaches his goal, the winner will be the one having the most letters in his color goal.

[1]  Rüdiger Verfürth,et al.  A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .

[2]  D. Braess,et al.  A posteriori estimators for obstacle problems by the hypercircle method , 2008 .

[3]  Wenbin Liu,et al.  A Posteriori Error Estimators for a Class of Variational Inequalities , 2000, J. Sci. Comput..

[4]  R. S. Falk.  Error estimates for the approximation of a class of variational inequalities , 1974 .

[5]  Carsten Carstensen,et al.  Averaging techniques yield reliable a posteriori finite element error control for obstacle problems , 2004, Numerische Mathematik.

[6]  Andreas Veeser,et al.  Convergent adaptive finite elements for the nonlinear Laplacian , 2002, Numerische Mathematik.

[7]  Carsten Carstensen,et al.  Convergence analysis of a conforming adaptive finite element method for an obstacle problem , 2007, Numerische Mathematik.

[8]  J. Tinsley Oden,et al.  Local a posteriori error estimators for variational inequalities , 1993 .

[9]  Claes Johnson,et al.  ADAPTIVE FINITE ELEMENT METHODS FOR THE OBSTACLE PROBLEM , 1992 .

[10]  Ricardo H. Nochetto,et al.  Data Oscillation and Convergence of Adaptive FEM , 2000, SIAM J. Numer. Anal..

[11]  Endre Süli,et al.  Adaptive finite element methods for differential equations , 2003, Lectures in mathematics.

[12]  H. Blum,et al.  An adaptive finite element discretisation¶for a simplified Signorini problem , 2000 .

[13]  Carsten Carstensen,et al.  Convergence analysis of an adaptive edge finite element method for the 2D eddy current equations , 2005, J. Num. Math..

[14]  Michael Hintermüller,et al.  Goal-oriented adaptivity in control constrained optimal control of partial differential equations , 2008, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[15]  J. Oden,et al.  A Posteriori Error Estimation in Finite Element Analysis , 2000 .

[16]  Franz-Theo Suttmeier,et al.  On a direct approach to adaptive FE-discretisations for elliptic variational inequalities , 2005, J. Num. Math..

[17]  Rob P. Stevenson,et al.  Optimality of a Standard Adaptive Finite Element Method , 2007, Found. Comput. Math..

[18]  Ricardo H. Nochetto,et al.  Residual type a posteriori error estimates for elliptic obstacle problems , 2000, Numerische Mathematik.

[19]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[20]  Dietrich Braess,et al.  A posteriori error estimators for obstacle problems – another look , 2005, Numerische Mathematik.

[21]  Kunibert G. Siebert,et al.  A Unilaterally Constrained Quadratic Minimization with Adaptive Finite Elements , 2007, SIAM J. Optim..

[22]  R. Hoppe,et al.  Adaptive multilevel methods for obstacle problems , 1994 .

[23]  Ricardo H. Nochetto,et al.  Fully Localized A posteriori Error Estimators and Barrier Sets for Contact Problems , 2004, SIAM J. Numer. Anal..

[24]  Andreas Veeser,et al.  Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems , 2001, SIAM J. Numer. Anal..

[25]  Claes Johnson,et al.  Computational Differential Equations , 1996 .

[26]  Ruo Li,et al.  Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems , 2002, SIAM J. Control. Optim..

[27]  W. Dörfler.  A convergent adaptive algorithm for Poisson's equation , 1996 .

[28]  Carsten Carstensen,et al.  Convergence analysis of an adaptive nonconforming finite element method , 2006, Numerische Mathematik.

[29]  Wolfgang Dahmen,et al.  Adaptive Finite Element Methods with convergence rates , 2004, Numerische Mathematik.

[30]  I. Babuska,et al.  The finite element method and its reliability , 2001 .

[31]  Carsten Carstensen,et al.  Error reduction and convergence for an adaptive mixed finite element method , 2006, Math. Comput..

[32]  Ricardo H. Nochetto,et al.  Pointwise a posteriori error control for elliptic obstacle problems , 2003, Numerische Mathematik.