DISCONTINUOUS GALERKIN DISCRETIZATION OF THE HEAT EQUATION IN ANY DIMENSION : THE SPECTRAL SYMBOL

Discontinuous Galerkin discretization of the heat equation in any dimension : The spectral symbol

[1]  Leonid Golinskii,et al.  The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences , 2007, J. Approx. Theory.

[2]  Carlo Garoni,et al.  Spectral Analysis and Spectral Symbol of d-variate $\mathbb Q_{\boldsymbol p}$ Lagrangian FEM Stiffness Matrices , 2015, SIAM J. Matrix Anal. Appl..

[3]  A. Quarteroni.  Numerical Models for Differential Problems , 2009 .

[4]  Hendrik Speleers,et al.  Robust and optimal multi-iterative techniques for IgA Galerkin linear systems , 2015 .

[5]  Vít Dolejší,et al.  Discontinuous Galerkin Method: Analysis and Applications to Compressible Flow , 2015 .

[6]  Hendrik Speleers,et al.  On the spectrum of stiffness matrices arising from isogeometric analysis , 2014, Numerische Mathematik.

[7]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[8]  Béatrice Rivière,et al.  Discontinuous Galerkin methods for solving elliptic and parabolic equations - theory and implementation , 2008, Frontiers in applied mathematics.

[9]  Carlo Garoni.  Spectral distribution of PDE discretization matrices from isogeometric analysis: the case of $L^1$ coefficients and non-regular geometry , 2018 .

[10]  Carlo Garoni,et al.  Generalized locally Toeplitz sequences : Theory and applications , 2017 .

[11]  Hendrik Speleers,et al.  Robust and optimal multi-iterative techniques for IgA Galerkin linear systems This is a preprint of a paper published in Comput. Methods Appl. Mech. Engrg. 284 (2015) 230264. , 2015 .

[12]  S. Serra Capizzano,et al.  Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations , 2003 .

[13]  Hendrik Speleers,et al.  Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods , 2017, Math. Comput..

[14]  Claes Johnson,et al.  Introduction to Adaptive Methods for Differential Equations , 1995, Acta Numerica.

[15]  Hendrik Speleers,et al.  Spectral analysis and spectral symbol of matrices in isogeometric collocation methods , 2015, Math. Comput..

[16]  Carlo Garoni,et al.  Tools for Determining the Asymptotic Spectral Distribution of non-Hermitian Perturbations of Hermitian Matrix-Sequences and Applications , 2015 .

[17]  Stefano Serra-Capizzano.  More Inequalities and Asymptotics for Matrix Valued Linear Positive Operators: the Noncommutative Case , 2002 .

[18]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[19]  Stefano Serra-Capizzano,et al.  The GLT class as a generalized Fourier analysis and applications , 2006 .

[20]  Stefano Serra Capizzano,et al.  Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions , 2016, Math. Comput..

[21]  Shinichi Kawahara.  Galerkin-type approximations which are discontinuous in time for parabolic equations in a variable domain , 1977 .

[22]  Hendrik Speleers,et al.  Symbol-Based Multigrid Methods for Galerkin B-Spline Isogeometric Analysis , 2017, SIAM J. Numer. Anal..

[23]  Paolo Tilli,et al.  A note on the spectral distribution of toeplitz matrices , 1998 .

[24]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[25]  J. Hesthaven,et al.  Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications , 2007 .

[26]  Arno B. J. Kuijlaars,et al.  Superlinear Convergence of Conjugate Gradients , 2001, SIAM J. Numer. Anal..

[27]  P. Raviart,et al.  On a Finite Element Method for Solving the Neutron Transport Equation , 1974 .

[28]  Hendrik Speleers,et al.  Lusin theorem, GLT sequences and matrix computations: An application to the spectral analysis of PDE discretization matrices , 2017 .

[29]  Gene H. Golub,et al.  Matrix computations , 1983 .