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Page 1242 of Mathematical Reviews Vol. , Issue 99b [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(B-GHNT-AN; Ghent) A variational approximation method for 2nd order elliptic eigenvalue problems in a composite structure with nonstandard boundary conditions.  ...  The authors carry out the finite element analysis of a class of eigenvalue problems with nonlocal boundary conditions of Robin type.  ... 
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On a variational approximation method for a class of elliptic eigenvalue problems in composite structures

M. Vanmaele, R. Van Keer
<span title="1996-07-01">1996</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
We consider a second-order elliptic eigenvalue problem on a convex polygonal domain, divided in M nonoverlapping subdomains.  ...  We present a general finite element method to obtain a numerical solution of the eigenvalue problem, starting from a nonstandard formally equivalent variational formulation in an abstract setting in product  ...  In the case of a triangular mesh on Ω i one has p k+1,K = p k,K , for all p ∈ P k (K), for all K ∈ T i hi . Consistent mass finite element method 4.1. Variational eigenvalue problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-96-00741-7">doi:10.1090/s0025-5718-96-00741-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3dsok4kqdfdhjkcvebg5bu5zu4">fatcat:3dsok4kqdfdhjkcvebg5bu5zu4</a> </span>
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The mathematics of finite elements and applications

<span title="">1989</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wu724rsyybdghixb2famiiw7jy" style="color: black;">International Journal of Engineering Science</a> </i> &nbsp;
This property, when used for solving elliptic boundary value problems, leads to a new approach to the discretization of boundary integral equations, which is not based upon the decomposition of the boundary  ...  been modified to yield simpler variational formulations for linear exterior boundary value J J  ...  On the other hand the method deals with boundary conditions and divergence conditions in a natural way.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0020-7225(89)90012-8">doi:10.1016/0020-7225(89)90012-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z6hknn325re4tbssbqqzmcketa">fatcat:z6hknn325re4tbssbqqzmcketa</a> </span>
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Singular perturbations and time scales in guidance and control of aerospace systems - A survey

D. S. Naidu, Anthony J. Calise
<span title="">2001</span> <i title="American Institute of Aeronautics and Astronautics (AIAA)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yekwqy6srncl5bew6tynp7vjsq" style="color: black;">Journal of Guidance Control and Dynamics</a> </i> &nbsp;
This is due to the fact that complex eigenvalues appear in the Hamiltonian matrix associated with the necessary conditions for optimality asso- ciated with the boundary layer analysis of these dynamics  ...  ., “Singular Perturbation Methods for Variational Problems in Aircraft Flight,” JEEE Transactions on Automatic ( Vol. AC-21, 1976, pp. 345-352 ’Calise, A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2514/3.22603">doi:10.2514/3.22603</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v76ixl3625hg5n7jeu3rzceqwq">fatcat:v76ixl3625hg5n7jeu3rzceqwq</a> </span>
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Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey

D. Subbaram Naidu, Anthony J. Calise
<span title="">2001</span> <i title="American Institute of Aeronautics and Astronautics (AIAA)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/yekwqy6srncl5bew6tynp7vjsq" style="color: black;">Journal of Guidance Control and Dynamics</a> </i> &nbsp;
This is due to the fact that complex eigenvalues appear in the Hamiltonian matrix associated with the necessary conditions for optimality asso- ciated with the boundary layer analysis of these dynamics  ...  ., “Singular Perturbation Methods for Variational Problems in Aircraft Flight,” JEEE Transactions on Automatic ( Vol. AC-21, 1976, pp. 345-352 ’Calise, A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2514/2.4830">doi:10.2514/2.4830</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qdfw6bvvxrawbmxoelk6ioc5uq">fatcat:qdfw6bvvxrawbmxoelk6ioc5uq</a> </span>
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High-order discretization of a stable time-domain integral equation for 3D acoustic scattering [article]

Alex H. Barnett, Leslie Greengard, Tom Hagstrom
<span title="2019-03-29">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation.  ...  The spatial discretization, of Nystr\"om type, uses Gaussian quadrature on panels combined with a special treatment of the weakly singular kernels arising in near-neighbor interactions.  ...  We are grateful for useful discussions with Charlie Epstein, Maciej Zworski, and Andrew Hassell.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.00076v1">arXiv:1904.00076v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ft3lacqrtnb37po3n5r3bi2xp4">fatcat:ft3lacqrtnb37po3n5r3bi2xp4</a> </span>
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Asymptotic Analysis and Synthesis in Mechanics of Solids and Nonlinear Dynamics [article]

I. V. Andrianov, H. Topol
<span title="2012-08-05">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed.  ...  While applying asymptotic methods as a rule the following situation appears: the existence of asymptotics for → 0 implies an existence of the asymptotics for →∞.  ...  (123) : σ = σ xx = σ xxxx = 0 for x = 0, ℓ. (124) BVP (123) , (124) is of the 6th order in spatial variable. Using PA we can obtain a modified continuous approximation of the 2nd order.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1106.1783v2">arXiv:1106.1783v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/onqbolqqvjf3tob3wgyouvk3hq">fatcat:onqbolqqvjf3tob3wgyouvk3hq</a> </span>
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Multigrid with Nonstandard Coarsening [article]

Kamala Liu, William D. Henshaw
<span title="2020-08-10">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We are motivated by the problem of developing high-order accurate numerical solvers for elliptic boundary value problems on complex geometry using overset grids.  ...  We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators.  ...  Introduction We are motivated by the solution of elliptic partial differential equations (PDE) and boundary value problems in complex geometry using composite overlapping grids.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.03885v1">arXiv:2008.03885v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3nrf74qzhbdqtcl4pzrrj3l4ne">fatcat:3nrf74qzhbdqtcl4pzrrj3l4ne</a> </span>
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Reviews and Descriptions of Tables and Books

<span title="1991-01-01">1991</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
Multivariate approximation methods have always been important for data interpolation and approximation, cubature, and for the numerical solution of boundary value problems (the finite element method).  ...  Morton, Difference methods for initial-value problems, 2nd ed. Interscience, New York, 1967. 3. G. Strang and G. J.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-91-99753-x">doi:10.1090/s0025-5718-91-99753-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h4r3r3alz5clji27zuaaps3zu4">fatcat:h4r3r3alz5clji27zuaaps3zu4</a> </span>
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Page 1535 of Mathematical Reviews Vol. 31, Issue Index [page]

<i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A variational approximation method for 2nd order elliptic eigenvalue problems in a composite structure with nonstandard boundary conditions.  ...  (with Van Keer, Roger) On a variational approximation method for 2nd order eigenvalue problems in a multi-component domain with nonlocal Dirichlet transition conditions.  ... 
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Multiscale and Wavelet Methods for Operator Equations [chapter]

Wolfgang Dahmen
<span title="">2003</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/vex472dtx5fadbic7anxo6uh5y" style="color: black;">Lecture notes in mathematics</a> </i> &nbsp;
The performance of an iterative scheme for a symmetric positive system is known to depend on the condition number of that system which in this case is the quotient of the maximal and minimal eigenvalue  ...  Although it will be explained later in a little bit more detail, what can be said about the condition numbers  ...  Scalar 2nd Order Elliptic Boundary Value Problem Suppose that Ω ⊂ IR d is a bounded (Lipschitz) domain and a(x) is a symmetric (bounded) matrix that is uniformly positive definite on Ω.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-39810-3_2">doi:10.1007/978-3-540-39810-3_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3zwrlw7tkbfydkonio7vljbpiq">fatcat:3zwrlw7tkbfydkonio7vljbpiq</a> </span>
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1. Solution of Partial Differential Equations on Vector and Parallel Computers [chapter]

<span title="">1985</span> <i title="Society for Industrial and Applied Mathematics"> Solution of Partial Differential Equations on Vector and Parallel Computers </i> &nbsp;
Their model problem is a second order elliptic equation with Dirichlet boundary conditions on the unit square, discretized by the five--point star and with the finite difference equations ordered red/black  ...  Other aspects which affect this will include the domain, the boundary conditions (and perhaps computational boundary conditions needed for hyperbolic equations and/or higher order methods), the form of  ...  "Possibilities and Problems with the Application of Vector Computers," German Research and Testing Establishment for Aerospace. Gehringer, E., Jones, A. and Segall, Z. [1982] .  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180725215815/https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19850008216.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7f/48/7f489c0ed200c3fddc0aab226b74a9cd8b9828a8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611971774.ch1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs [article]

Kristin Kirchner
<span title="2018-04-19">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove well-posedness of the deterministic variational problem for the second moment, improving an earlier result.  ...  For the canonical examples with additive noise (Ornstein-Uhlenbeck process) or multiplicative noise (geometric Brownian motion) we derive these deterministic equations in variational form and discuss their  ...  For the following numerical experiment we set T := 1, H := L2 (0, 1) equipped with the usual inner product, and A := −( · )00 with homogeneous Dirichlet boundary conditions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1611.02164v2">arXiv:1611.02164v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dyt4vpjxjbh3lonwmbwp3yaoie">fatcat:dyt4vpjxjbh3lonwmbwp3yaoie</a> </span>
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Page 1879 of Mathematical Reviews Vol. , Issue Subject Index [page]

<i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(with Hristov, A. H.) On the variational aspects for elliptic problems with parameter on the boundary.  ...  (with Ferreira, José Augusto Mendes) A nonstandard linear finite element method for a planar elasticity problem.  ... 
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HOMOGENIZATION OF ELASTIC WAVES IN FLUID-SATURATED POROUS MEDIA USING THE BIOT MODEL

ALEXANDER MIELKE, EDUARD ROHAN
<span title="">2013</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ll562xhqsnhdfeim3fphvna7a4" style="color: black;">Mathematical Models and Methods in Applied Sciences</a> </i> &nbsp;
Using the two-scale homogenization method we obtain the limit two-scale problem and prove the existence and uniqueness of its weak solutions.  ...  The Laplace transformation in time is used to decouple the macroscopic and microscopic scales.  ...  The research of A.M. was partially supported by DFG through the SFB 910, subproject A5 "Pattern formation in systems with multiple scales".  ... 
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