10,451 research outputs found
Unified analysis of HDG methods using scalar and vector hybrid variables
In this paper, hybridizable discontinuous Galerkin (HDG) methods using scalar
and vector hybrid variables for steady-state diffusion problems are considered.
We propose a unified framework to analyze the methods, where both the hybrid
variables are treated as double-valued functions. If either of them is single
valued, the well-posedness is ensured under some assumptions on approximation
spaces. Moreover, we prove that all methods are superconvergent, based on the
so-called -decomposition theory. Numerical results are presented to validate
our theoretical results.Comment: 16 page
Final Goods Substitutability and Economic Growth
In this paper, I investigate the effect of substitutability among final goods on welfare growth under the environment that productivity growth in each industry is not independent of one another. In such an environment, less substitutability is favorable to the welfare growth rate and the steady state welfare level, contrasting to Baumol (1967) and Lucas (1988).
Analysis of the Size of the Carcinoembryonic Antigen (CEA) Gene Family
Five members of the human CEA gene family [human pregnancy-specific β1-glycoprotein (PSβG), hsCGM1, 2, 3 and 4] have been isolated and identified through sequencing the exons containing their N-terminal domains. Sequence comparisons with published data for CEA and related molecules reveal the existence of highly-conserved gene subgroups within the CEA family. Together with published data eleven CEA family members have so far been determined. Apart from the highly conserved coding sequences, these genes also show strong sequence conservation in their introns, indicating a duplication of whole gene units during the evolution of the CEA gene family
Penalty method with Crouzeix-Raviart approximation for the Stokes equations under slip boundary condition
The Stokes equations subject to non-homogeneous slip boundary conditions are
considered in a smooth domain . We
propose a finite element scheme based on the nonconforming P1/P0 approximation
(Crouzeix-Raviart approximation) combined with a penalty formulation and with
reduced-order numerical integration in order to address the essential boundary
condition on . Because the
original domain must be approximated by a polygonal (or polyhedral)
domain before applying the finite element method, we need to take
into account the errors owing to the discrepancy , that
is, the issues of domain perturbation. In particular, the approximation of
by makes it non-trivial whether we
have a discrete counterpart of a lifting theorem, i.e., right-continuous
inverse of the normal trace operator ; . In this paper
we indeed prove such a discrete lifting theorem, taking advantage of the
nonconforming approximation, and consequently we establish the error estimates
and for the velocity in
the - and -norms respectively, where if and
if . This improves the previous result [T. Kashiwabara et
al., Numer. Math. 134 (2016), pp. 705--740] obtained for the conforming
approximation in the sense that there appears no reciprocal of the penalty
parameter in the estimates.Comment: 21 page
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