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$L^{2}$ -error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

Thomas Apel, Dieter Sirch (2011)

Applications of Mathematics

An $L^{2}$ -estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space.

$L^{2}$ -error estimates of the extrapolated Crank-Nicolson discontinuous Galerkin approximations for nonlinear Sobolev equations.

Ohm, Mi Ray, Lee, Hyun Young, Shin, Jun Yong (2010)

Journal of Inequalities and Applications [electronic only]

$L^{2}$ -stability of the upwind first order finite volume scheme for the Maxwell equations in two and three dimensions on arbitrary unstructured meshes

Serge Piperno (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

$L_{\infty}$ -convergence of finite element Galerkin approximations for parabolic problems

Joachim A. Nitsche (1979)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

$L_{\infty}$ -convergence of saddle-point approximations for second order problems

Reinhard Scholz (1977)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

$L$ -curve curvature bounds via Lanczos bidiagonalization.

Calvetti, D., Hansen, P.C., Reichel, L. (2002)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

$L^{\infty}$ -error analysis for a system of quasivariational inequalities with noncoercive operators.

Boulbrachene, Messaoud, Saadi, Samira (2006)

Journal of Inequalities and Applications [electronic only]

$L^{\infty}$ -error estimate for a discrete two-sided obstacle problem and multilevel projective algorithm.

Jiang, Ying-Jun, Zeng, Jin-Ping (2006)

Lobachevskii Journal of Mathematics

$L^{\infty}$ -error estimate for a system of elliptic quasivariational inequalities.

Boulbrachene, M., Haiour, M., Saadi, S. (2003)

International Journal of Mathematics and Mathematical Sciences

$L^{\infty}$ -error estimates for a class of semilinear elliptic variational inequalities and quasi-variational inequalities.

Boulbrachene, M., Cortey-Dumont, P., Miellou, J.C. (2001)

International Journal of Mathematics and Mathematical Sciences

$L_{\infty}$ -error estimates for variational inequalities with Hölder continuous obstacle

Stefano Finzi Vita (1982)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

$L^{\infty} (L^{2})$ and $L^{\infty} (L^{\infty})$ error estimates for mixed methods for integro-differential equations of parabolic type

Ziwen Jiang (1999)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

$L_{p}$ - and $S_{p, q}^{r} B$ -discrepancy of (order 2) digital nets

Lev Markhasin (2015)

Acta Arithmetica

Dick proved that all dyadic order 2 digital nets satisfy optimal upper bounds on the $L_{p}$ -discrepancy. We prove this for arbitrary prime base b with an alternative technique using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds on the discrepancy function in Besov spaces with dominating mixed smoothness for a certain parameter range, and enlarge that range for order 2 digital nets. The discrepancy function in Triebel-Lizorkin and Sobolev spaces with dominating mixed...

L... Stability of Finite Element Approximations to Elliptic Gradient Equations.

Joseph W. Jerome, Th. Kerkhoven (1990)

Numerische Mathematik

$L U$ factorizations

Cony M. Lau, Thomas L. Markham (1979)

Czechoslovak Mathematical Journal

L1 and L... Uniform Convergence of a Difference Scheme for a Semilinear Singular Perturbation Problem.

Eugene O'Riordan, Martin Stynes (1986/1987)

Numerische Mathematik

L1-Approximation verallgemeinerter konvexer Funktionen durch Splines mit freien Knoten.

Kurt Jetter (1978/1979)

Mathematische Zeitschrift

L2 Error Estimates for Finite Elements with Interpolated Boundary Conditions.

Alan E. Berger (1973)

Numerische Mathematik

L2 Estimates for the Finite Element Method for the Dirichlet Problem with Singular Data.

Eduardo Casas (1985)

Numerische Mathematik

L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, Mengping Zhang (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

 We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.

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