Finite element adaptive method for hypersonic thermochemical nonequilibrium flows

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1294-1302
Author(s):  
Djaffar Ait-Ali-Yahia ◽  
Wagdi G. Habashi
Keyword(s):  
Finite Element ◽  
Adaptive Method ◽  
Nonequilibrium Flows

Finite Element Adaptive Method for Hypersonic Thermochemical Nonequilibrium Flows

AIAA Journal ◽  
10.2514/2.260 ◽  
1997 ◽  
Vol 35 (8) ◽  
pp. 1294-1302 ◽  
Author(s):  
Djaffar Ait-Ali-Yahia ◽  
Wagdi G. Habashi
Keyword(s):  
Finite Element ◽  
Adaptive Method ◽  
Nonequilibrium Flows

scholarly journals CONVERGENT ADAPTIVE FINITE ELEMENT METHODS FOR PHOTONIC CRYSTAL APPLICATIONS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250028
Author(s):  
STEFANO GIANI
Keyword(s):  
Finite Element ◽  
Photonic Crystal ◽  
Eigenvalue Problems ◽  
Adaptive Methods ◽  
Discontinuous Coefficients ◽  
Adaptive Method ◽  
Adaptive Finite Element Method ◽  
Global Maximum ◽  
Adaptive Finite Element ◽  
Adaptive Finite Element Methods

We prove the convergence of an adaptive finite element method for computing the band structure of two-dimensional periodic photonic crystals with or without compact defects in both the TM and TE polarization cases. These eigenvalue problems involve non-coercive elliptic operators with discontinuous coefficients. The error analysis extends the theory of convergence of adaptive methods for elliptic eigenvalue problems to photonic crystal problems, and in particular deals with various complications which arise essentially from the lack of coercivity of the elliptic operator with discontinuous coefficients. We prove the convergence of the adaptive method in an oscillation-free way and with no extra assumptions on the initial mesh, beside the conformity and shape regularity. Also we present and prove the convergence of an adaptive method to compute efficiently an entire band in the spectrum. This method is guaranteed to converge to the correct global maximum and minimum of the band, which is a very useful piece of information in practice. Our numerical results cover both the cases of periodic structures with and without compact defects.

scholarly journals Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method

2013 ◽  
Vol 13 (5) ◽  
pp. 1277-1244 ◽  
Author(s):  
Xue Jiang ◽  
Peijun Li ◽  
Weiying Zheng
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Adaptive Method ◽  
Two Dimensions ◽  
Adaptive Finite Element ◽  
Acoustic Wave Scattering

AbstractConsider the acoustic wave scattering by an impenetrable obstacle in two dimensions, where the wave propagation is governed by the Helmholtz equation. The scattering problem is modeled as a boundary value problem over a bounded domain. Based on the Dirichlet-to-Neumann (DtN) operator, a transparent boundary condition is introduced on an artificial circular boundary enclosing the obstacle. An adaptive finite element based on a posterior error estimate is presented to solve the boundary value problem with a nonlocal DtN boundary condition. Numerical experiments are included to compare with the perfectly matched layer (PML) method to illustrate the competitive behavior of the proposed adaptive method.

NUMERICAL SOLUTION FOR THE NONLINEAR EMDEN–FOWLER TYPE EQUATIONS BY A FOURTH-ORDER ADAPTIVE METHOD

2013 ◽  
Vol 11 (01) ◽  
pp. 1350052 ◽  
Author(s):  
S. A. KHURI ◽  
A. SAYFY
Keyword(s):  
Finite Element ◽  
Numerical Solution ◽  
Rate Of Convergence ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Adaptive Method ◽  
B Splines ◽  
Special Cases ◽  
Collocation Approach

A finite element collocation approach, based on cubic B-splines, is manipulated for obtaining numerical solutions of a generalized form of the Emden–Fowler type equations. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order by using the double-mesh principle. The efficiency of the scheme is tested on a number of examples which represent special cases of the problem under consideration. The results are compared with analytical and other numerical solutions that are available in the literature. The proposed method reveals that the outcomes are reliable and very accurate when contrasted with other existing methods.

scholarly journals Quasi-optimal adaptive hybridized  mixed finite element methods for linear elasticity

2021 ◽  
Author(s):  
Yuwen Li
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Adaptive Algorithm ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Mixed Finite Element ◽  
Adaptive Methods ◽  
Adaptive Method ◽  
A Posteriori ◽  
Numer Math

For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu: Numer.~Math., 141 (2019), pp.~569--604]. The main ingredients in the analysis consist of a discrete a posteriori upper bound and a quasi-orthogonality result for the stress field under the mixed boundary condition. Compared with existing adaptive methods, the proposed adaptive algorithm could be directly applied to the traction boundary condition and be easily implemented.

Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell’s Equations

2013 ◽  
Vol 13 (2) ◽  
pp. 559-582 ◽  
Author(s):  
Xue Jiang ◽  
Linbo Zhang ◽  
Weiying Zheng
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Adaptive Methods ◽  
Adaptive Method ◽  
Adaptive Finite Element ◽  
Adaptive Finite Element Methods ◽  
Time Harmonic

AbstractIn this paper, hp-adaptive finite element methods are studied for time-harmonic Maxwell’s equations. We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates. Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities, edge singularities, and an engineering benchmark problem of Maxwell’s equations. The hp-adaptive methods show much better performance than the h-adaptive method.

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