A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
暂无分享,去创建一个
[1] Serge Prudhomme,et al. On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors , 1999 .
[2] W. Rheinboldt,et al. Error Estimates for Adaptive Finite Element Computations , 1978 .
[3] Assyr Abdulle,et al. Finite Element Heterogeneous Multiscale Methods with Near Optimal Computational Complexity , 2008, Multiscale Model. Simul..
[4] Assyr Abdulle,et al. A posteriori error analysis of the heterogeneous multiscale method for homogenization problems , 2009 .
[5] Endre Süli,et al. Adaptive finite element methods for differential equations , 2003, Lectures in mathematics.
[6] G. Rozza,et al. ON THE APPROXIMATION OF STABILITY FACTORS FOR GENERAL PARAMETRIZED PARTIAL DIFFERENTIAL EQUATIONS WITH A TWO-LEVEL AFFINE DECOMPOSITION , 2012 .
[7] Alfio Quarteroni,et al. A modular lattice boltzmann solver for GPU computing processors , 2012 .
[8] Ricardo H. Nochetto,et al. Convergence of Adaptive Finite Element Methods , 2002, SIAM Rev..
[9] Assyr Abdulle,et al. Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems , 2012, J. Comput. Phys..
[10] M. Larson,et al. Adaptive variational multiscale methods based on a posteriori error estimation: Energy norm estimates for elliptic problems , 2007 .
[11] E Weinan,et al. Finite difference heterogeneous multi-scale method for homogenization problems , 2003 .
[12] Grégoire Allaire,et al. The mathematical modeling of composite materials , 2002 .
[13] Ivo Babuska,et al. Generalized p-FEM in homogenization , 2000, Numerische Mathematik.
[14] Assyr Abdulle,et al. Multiscale method based on discontinuous Galerkin methods for homogenization problems , 2008 .
[15] Antoine Gloria,et al. Reduction of the resonance error---Part 1: Approximation of homogenized coefficients , 2011 .
[16] P. Henning,et al. posteriori error estimation for a heterogeneous multiscale method for monotone operators and beyond a periodic setting , 2011 .
[17] Mark Ainsworth,et al. Guaranteed computable bounds on quantities of interest in finite element computations , 2012 .
[18] Assyr Abdulle,et al. A priori and a posteriori error analysis for numerical homogenization: a unified framework , 2011 .
[19] E Weinan,et al. The Heterognous Multiscale Methods , 2003 .
[20] M. Larson,et al. Adaptive Variational Multiscale Methods Based on A Posteriori Error Estimation: Duality Techniques for Elliptic Problems , 2005 .
[21] Josef Stoer,et al. Numerische Mathematik 1 , 1989 .
[22] Kunibert G. Siebert,et al. Design of Adaptive Finite Element Software - The Finite Element Toolbox ALBERTA , 2005, Lecture Notes in Computational Science and Engineering.
[23] A. Quarteroni,et al. Model reduction techniques for fast blood flow simulation in parametrized geometries , 2012, International journal for numerical methods in biomedical engineering.
[24] S.,et al. " Goal-Oriented Error Estimation and Adaptivity for the Finite Element Method , 1999 .
[25] Assyr Abdulle,et al. Heterogeneous Multiscale Methods with Quadrilateral Finite Elements , 2006 .
[26] T. Hughes. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .
[27] Thomas Grätsch,et al. Review: A posteriori error estimation techniques in practical finite element analysis , 2005 .
[28] Mario Ohlberger,et al. A Posteriori Error Estimates for the Heterogeneous Multiscale Finite Element Method for Elliptic Homogenization Problems , 2005, Multiscale Model. Simul..
[29] Gianluigi Rozza,et al. A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks , 2012 .
[30] Assyr Abdulle,et al. A short and versatile finite element multiscale code for homogenization problems , 2009 .
[31] E Weinan,et al. The heterogeneous multiscale method* , 2012, Acta Numerica.
[32] Assyr Abdulle,et al. On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM , 2005, Multiscale Model. Simul..
[33] E. Giorgi,et al. Sulla convergenza degli integrali dell''energia per operatori ellittici del secondo ordine , 1973 .
[34] Ronald Cools,et al. Constructing cubature formulae: the science behind the art , 1997, Acta Numerica.
[35] E Weinan,et al. Heterogeneous multiscale method: A general methodology for multiscale modeling , 2003 .
[36] George Papanicolaou,et al. A Framework for Adaptive Multiscale Methods for Elliptic Problems , 2008, Multiscale Model. Simul..
[37] Assyr Abdulle,et al. The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs , 2009 .
[38] Alfio Quarteroni,et al. Numerical Approximation of Internal Discontinuity Interface Problems , 2013, SIAM J. Sci. Comput..
[39] Achim Nonnenmacher,et al. Adaptive Finite Element Methods for Multiscale Partial Differential Equations , 2011 .
[40] Ricardo H. Nochetto,et al. A safeguarded dual weighted residual method , 2008 .
[41] Hengguang Li,et al. The effect of numerical integration on the finite element approximation of linear functionals , 2011, Numerische Mathematik.
[42] Thomas Y. Hou,et al. Convergence of a multiscale finite element method for elliptic problems with rapidly oscillating coefficients , 1999, Math. Comput..
[43] Rüdiger Verfürth,et al. A posteriori error estimation and adaptive mesh-refinement techniques , 1994 .
[44] Assyr Abdulle. Discontinuous Galerkin finite element heterogeneous multiscale method for elliptic problems with multiple scales , 2012, Math. Comput..
[46] A. Abdulle. ANALYSIS OF A HETEROGENEOUS MULTISCALE FEM FOR PROBLEMS IN ELASTICITY , 2006 .
[47] Rolf Rannacher,et al. An optimal control approach to a posteriori error estimation in finite element methods , 2001, Acta Numerica.
[48] A. Bensoussan,et al. Asymptotic analysis for periodic structures , 1979 .
[49] I. Babuska,et al. Special finite element methods for a class of second order elliptic problems with rough coefficients , 1994 .
[50] O. A. Ladyzhenskai︠a︡. Boundary value problems of mathematical physics , 1967 .
[51] G. Nguetseng. A general convergence result for a functional related to the theory of homogenization , 1989 .
[52] Xiang Ma,et al. A stochastic mixed finite element heterogeneous multiscale method for flow in porous media , 2011, J. Comput. Phys..
[53] J. Tinsley Oden,et al. MultiScale Modeling of Physical Phenomena: Adaptive Control of Models , 2006, SIAM J. Sci. Comput..
[54] E. Weinan,et al. Analysis of the heterogeneous multiscale method for elliptic homogenization problems , 2004 .
[55] Yalchin Efendiev,et al. Multiscale Finite Element Methods: Theory and Applications , 2009 .
[56] Assyr Abdulle. Reduced basis heterogeneous multiscale methods , 2015 .
[57] Philippe G. Ciarlet,et al. THE COMBINED EFFECT OF CURVED BOUNDARIES AND NUMERICAL INTEGRATION IN ISOPARAMETRIC FINITE ELEMENT METHODS , 1972 .
[58] H. Schmid. On cubature formulae with a minimal number of knots , 1978 .
[59] Assyr Abdulle,et al. Adaptive finite element heterogeneous multiscale method for homogenization problems , 2011 .
[60] J. Z. Zhu,et al. The finite element method , 1977 .
[61] Christoph Schwab,et al. High-Dimensional Finite Elements for Elliptic Problems with Multiple Scales , 2005, Multiscale Modeling & simulation.
[62] Gianluigi Rozza,et al. Numerical Simulation of Sailing Boats: Dynamics, FSI, and Shape Optimization , 2012 .
[63] Pablo J. Blanco,et al. A two-level time step technique for the partitioned solution of one-dimensional arterial networks , 2012 .
[64] V. Kouznetsova,et al. Multiscale modeling of residual stresses in isotropic conductive adhesives with nano particles , 2012 .
[65] F. John. Partial differential equations , 1967 .
[66] I. Babuska,et al. Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods , 1983 .
[67] Igor E. Shparlinski. Report on global methods for combinatorial isoperimetric problems , 2005, Math. Comput..
[68] J. Oden,et al. A Posteriori Error Estimation in Finite Element Analysis , 2000 .
[69] Carsten Carstensen,et al. P2Q2Iso2D = 2D isoparametric FEM in Matlab , 2006 .
[70] T. Hughes,et al. The variational multiscale method—a paradigm for computational mechanics , 1998 .
[71] M. Giles,et al. Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality , 2002, Acta Numerica.
[72] J. Guermond,et al. Theory and practice of finite elements , 2004 .
[73] Assyr Abdulle,et al. Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces , 2005, Multiscale Model. Simul..
[74] G. M.,et al. Partial Differential Equations I , 2023, Applied Mathematical Sciences.
[75] D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics , 1995 .
[76] V. Zhikov,et al. Homogenization of Differential Operators and Integral Functionals , 1994 .
[77] G. Gustafson,et al. Boundary Value Problems of Mathematical Physics , 1998 .
[78] E. Vanden-Eijnden,et al. The Heterogeneous Multiscale Method: A Review , 2007 .
[79] I. Babuska,et al. The finite element method and its reliability , 2001 .