An adaptive hp-version of the multilevel particle–partition of unity method
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[1] E. H. Jarow. Clouds , 1931, Nature.
[2] J. Nitsche. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind , 1971 .
[3] D. Griffin,et al. Finite-Element Analysis , 1975 .
[4] W. Rheinboldt,et al. Error Estimates for Adaptive Finite Element Computations , 1978 .
[5] Wolfgang Hackbusch,et al. Multi-grid methods and applications , 1985, Springer series in computational mathematics.
[6] Jinchao Xu,et al. Iterative Methods by Space Decomposition and Subspace Correction , 1992, SIAM Rev..
[7] I. I. Bakelʹman,et al. Geometric Analysis and Nonlinear Partial Differential Equations , 1993 .
[8] I. Babuska,et al. Special finite element methods for a class of second order elliptic problems with rough coefficients , 1994 .
[9] T. Belytschko,et al. Crack propagation by element-free Galerkin methods , 1995 .
[10] J. Oden,et al. H‐p clouds—an h‐p meshless method , 1996 .
[11] T. Belytschko,et al. Nodal integration of the element-free Galerkin method , 1996 .
[12] I. Babuska,et al. The Partition of Unity Method , 1997 .
[13] Ted Belytschko,et al. Enforcement of essential boundary conditions in meshless approximations using finite elements , 1996 .
[14] C. Schwab. P- and hp- finite element methods : theory and applications in solid and fluid mechanics , 1998 .
[15] Ted Belytschko,et al. Elastic crack growth in finite elements with minimal remeshing , 1999 .
[16] Ted Belytschko,et al. A finite element method for crack growth without remeshing , 1999 .
[17] Ted Belytschko,et al. Numerical integration of the Galerkin weak form in meshfree methods , 1999 .
[18] Ivo Babuška,et al. Generalized finite element methods for three-dimensional structural mechanics problems , 2000 .
[19] Michael Griebel,et al. A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs , 2000, SIAM J. Sci. Comput..
[20] I. Babuska,et al. The design and analysis of the Generalized Finite Element Method , 2000 .
[21] Jiun-Shyan Chen,et al. A stabilized conforming nodal integration for Galerkin mesh-free methods , 2001 .
[22] I. Babuska,et al. The generalized finite element method , 2001 .
[23] Barbara I. Wohlmuth,et al. On residual-based a posteriori error estimation in hp-FEM , 2001, Adv. Comput. Math..
[24] Ted Belytschko,et al. Arbitrary discontinuities in finite elements , 2001 .
[25] T. Liszka,et al. A generalized finite element method for the simulation of three-dimensional dynamic crack propagation , 2001 .
[26] Jiun-Shyan Chen,et al. Non‐linear version of stabilized conforming nodal integration for Galerkin mesh‐free methods , 2002 .
[27] Michael Griebel,et al. A Particle-Partition of Unity Method-Part II: Efficient Cover Construction and Reliable Integration , 2001, SIAM J. Sci. Comput..
[28] Michael Griebel,et al. A Particle-Partition of Unity Method-Part III: A Multilevel Solver , 2002, SIAM J. Sci. Comput..
[29] Michael Griebel,et al. Meshfree Methods for Partial Differential Equations , 2002 .
[30] Michael Griebel,et al. A Particle-Partition of Unity Method Part V: Boundary Conditions , 2003 .
[31] I. Babuska,et al. Acta Numerica 2003: Survey of meshless and generalized finite element methods: A unified approach , 2003 .
[32] Marc Alexander Schweitzer,et al. A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations , 2003, Lecture Notes in Computational Science and Engineering.
[33] I. Babuska,et al. Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids , 2003 .
[34] G. Fasshauer. Meshfree Methods , 2004 .
[35] Ivo Babuška,et al. p‐version of the generalized FEM using mesh‐based handbooks with applications to multiscale problems , 2004 .
[36] Thomas Gerstner,et al. Numerical integration using sparse grids , 2004, Numerical Algorithms.
[37] Michael Griebel,et al. Meshfree Methods for Partial Differential Equations IV , 2005 .
[38] Pedro Díez,et al. Subdomain-based flux-free a posteriori error estimators , 2006 .
[39] Ivo Babuška,et al. A posteriori error estimation for generalized finite element methods , 2006 .
[40] F. Otto,et al. Uniform Energy Distribution for Minimizers of an Isoperimetric Problem Containing Long-range Interactions ∗ , 2007 .
[41] Carlos Armando Duarte,et al. A high‐order generalized FEM for through‐the‐thickness branched cracks , 2007 .
[42] M. Puso,et al. A New Stabilized Nodal Integration Approach , 2007 .
[43] S. Albeverio,et al. Description of Derivations on Measurable Operator Algebras of Type I , 2007, 0710.3344.
[44] Michael Griebel,et al. A Particle-Partition of Unity Method Part VII: Adaptivity , 2007 .
[45] Michael Griebel,et al. A sparse grid space-time discretization scheme for parabolic problems , 2007, Computing.
[46] C. Duarte,et al. Analysis and applications of a generalized finite element method with global-local enrichment functions , 2008 .
[47] Jens Frehse. An irregular complex valued solution to a scalar uniformly elliptic equation , 2008 .
[48] Jens Frehse,et al. Hölder continuity for the displacements in isotropic and kinematic hardening with von Mises yield criterion , 2008 .
[49] Thomas Gerstner,et al. A general asset–liability management model for the efficient simulation of portfolios of life insurance policies , 2008 .
[50] Marc Alexander Schweitzer,et al. A Particle-Partition of Unity Method Part VIII: Hierarchical Enrichment , 2008 .
[51] Angela Kunoth,et al. A wavelet-based nested iteration–inexact conjugate gradient algorithm for adaptively solving elliptic PDEs , 2008, Numerical Algorithms.
[52] Werner Mueller. Groups and Analysis: Weyl's law in the theory of automorphic forms , 2007, 0710.2319.
[53] S. Albeverio,et al. On fine fractal properties of generalized infinite Bernoulli convolutions , 2008 .
[54] Michael Griebel,et al. On a Constructive Proof of Kolmogorov’s Superposition Theorem , 2009 .
[55] Moritz Kassmann,et al. A priori estimates for integro-differential operators with measurable kernels , 2009 .
[56] S. Albeverio,et al. Algebras of unbounded operators over the ring of measurable functions and their derivations and automorphisms , 2007, 0710.5839.
[57] Jens Frehse,et al. Existence of a Regular Periodic Solution to the Rothe Approximation of the Navier—Stokes Equation in Arbitrary Dimension , 2009 .
[58] Marc Alexander Schweitzer,et al. Multilevel particle-partition of unity method , 2011, Numerische Mathematik.