椭圆方程有限元方法的整体超收敛及其应用(英文版)

.2.6 new stability analysis via effective condition number.
2.6.1 computational formulas
2.6.2 bounds of effective condition number
2.7 numerical experiments and concluding remarks
chapter 3 biquadratic lagrange elements
3.1 introduction
3.2 biquadratic lagrange elements
3.3 global superconvergence
3.3.1 new error estimates
3.3.2 proof of theorem 3.3.1
3.3.3 proof of theorem 3.3.2
3.3.4 error bounds for q8 elements
3.4 numerical experiments and discussions
3.4.1 global superconvergence
3.4.2 special case of h= k and
3.4.3 comparisons
3.4.4 relation between uh and
3.5 concluding remarks
chapter 4 simplified hybrid method for motz's problems
4.1 introduction
4.2 simplified hybrid combined methods
4.3 lagrange rectangular elements
4.4 adini's elements
4.5 concluding remarks
chapter 5 finite difference methods for singularity problem
5.1 introduction
5.2 the shortley-weller difference approximation
5.3 analysis for ud with no error of divergence integration
5.4 analysis for uh with approximation of divergence integration..
5.5 numerical verification on reduced convergence rates
5.5.1 the model on stripe domains
5.5.2 the richardson extrapolation and the least squares method
5.6 concluding remarks
chapter 6 basic error estimates for biharmonic equations ..
chapter 7 stability analysis and superconvergence of blending
problems
7.1 introduction
7.2 description of numerical methods
7.3 stability analysis
7.3.1 optimal convergence rates and the uniform v-elliptic inequality.
7.3.2 bounds of condition number
7.3.3 proof for theorem 7.3.4
7.4 global superconvergence
7.5 numerical experiments and other kinds of superconvergence.. -
7.5.1 verification of the analysis in section 7.3 and section 7.4
7.5.2 new superconvergence of average nodal solutions
7.5.3 superconvergence of l-norm
7.5.4 global superconvergence of the a posteriori interpolant solutions
7.6 concluding remarks
chapter 8 blending problems in 3d with periodical boundary
conditions
8.1 introduction
8.2 biharmouic equations
8.2.1 description of numerical methods
8.2.2 global superconvergence
8.3 the bph-fem for blending surfaces
8.4 optimal convergence and numerical stability
8.5 superconvergence
chapter 9 lower bounds of leading eigenvalues
9.1 introduction
9.1.1 bilinear element q1
9.1.2 rotated q1 element (qot)
9.1.3 extension of rotated qz element (eqrzt)
9.1.4 wilson's element
9.2 basic theorems
9.3 bilinea elements
9.4 qot and eqrlt elements
9.4.1 proof of lemma 9.4.1
9.4.2 proof of lemma 9.4.2
9.4.3 proof of lemma 9.4.3
9.4.4 proof of lemma 9.4.4
9.5 wilson's element
9.5.1 proof of lemma 9.5.1
9.5.2 proof of lemma 9.5.2
9.5.3 proof of lemma 9.5.3 and lemma 9.5.4
9.6 expansions for eigenfunctiens
9.7 numerical experiments
9.7.1 function p=1
9.7.2 function p=0
9.7.3 numerical conclusions
chapter 10 eigenvalue problems with periodical boundary conditions
10.1 introduction
10.2 periodic boundary conditions
10.3 adini's elements for eigenvalue problems
10.4 error analysis for poisson's equation
10.5 superconvergence for eigenvalue problems
10.6 applications to other kinds of fems
10.6.1 bi-quadratic lagrange elements
10.6.2 triangular elements
10.7 numerical results
10.8 concluding remarks
chapter 11 semilinear problems
11.1 introduction
11.2 parameter-dependent semilinear problems
11.3 basic theorems for superconvergence of fems
11.4 superconvergence of bi-p(] 2)-lagrange elements
11.5 a continuation algorithm using adini's elements
11.6 conclusions
chapter 12 epilogue
12.1 basic framework of global superconvergence
12.2 some results on integral identity analysis
12.3 some results on global superconvergence
bibliography
index