SUPERCONVERGENCE STUDIES OF QUADRILATERAL NONCONFORMING ROTATED Q1 ELEMENTS

A CMOS oscillator is disclosed using an inverter in which a pair of control terminals are employed to invoke various sized devices which control the flow of current. The inverter gain is determined by the size of the CMOS devices employed. A tuned circuit coupled to the inverter causes it to oscillate at the frequency of parallel resonance. The control terminals are coupled to the inverter invoke transistors that are sized as desired to establish the current flow and gain in the inverter. The current flow is controlled to optimize the gain of the inverter in terms of the frequency of oscillation. A Schmitt trigger can be employed to clean up the oscillator output for digital clock source applications.

[1]  Zhongci Shi A convergence condition for the quadrilateral Wilson element , 1984 .

[2]  Bo Li,et al.  Nonconforming finite element approximation of crystalline microstructure , 1998, Math. Comput..

[3]  Douglas N. Arnold,et al.  Approximation by quadrilateral finite elements , 2000, Math. Comput..

[4]  Zhimin Zhang,et al.  Analysis of recovery type a posteriori error estimators for mildly structured grids , 2003, Math. Comput..

[5]  Stefan Turek,et al.  Efficient Solvers for Incompressible Flow Problems - An Algorithmic and Computational Approach , 1999, Lecture Notes in Computational Science and Engineering.

[6]  Dongwoo Sheen,et al.  Nonconforming quadrilateral finite elements:¶a correction , 2000 .

[7]  P. Ming,et al.  TWO NONCONFORMING QUADRILATERAL ELEMENTS FOR THE REISSNER–MINDLIN PLATE , 2005 .

[8]  Zhangxin Chen,et al.  On the implementation of mixed methods as nonconforming methods for second-order elliptic problems , 1995 .

[9]  Dongwoo Sheen,et al.  Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems , 1999 .

[10]  Q. Lin,et al.  Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation , 2005 .

[11]  D. Kershaw Differencing of the diffusion equation in Lagrangian hydrodynamic codes , 1981 .

[12]  Zhong-Ci Shi,et al.  NONCONFORMING ROTATED ${\mathcal Q}_1$ ELEMENT FOR REISSNER–MINDLIN PLATE , 2001 .

[13]  P. Kloucek,et al.  The Three Dimensional Non-conforming Finite Element Solution of the Chapman-Ferraro Problem , 1999 .

[14]  Lutz Tobiska,et al.  The streamline–diffusion method for nonconforming Qrot1 elements on rectangular tensor–product meshes , 2001 .

[15]  R. Rannacher,et al.  Simple nonconforming quadrilateral Stokes element , 1992 .

[16]  Miloš Zlámal,et al.  Superconvergence and reduced integration in the finite element method , 1978 .

[17]  Uwe Risch,et al.  Superconvergence of a nonconforming low order finite element , 2005 .

[18]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[19]  Zhong-Ci Shi,et al.  Quadrilateral mesh revisited , 2002 .

[20]  Bo Li,et al.  Analysis of a class of nonconforming finite elements for crystalline microstructures , 1996, Math. Comput..