Publications

Technical reports submitted for publication

[1] Quasi-optimal approximation of surface based Lagrange multipliers in finite element methods

J.M. Melenk, B. Wohlmuth
ASC Report 13/2011

[2] Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: a roadmap

J.M. Melenk, C. Xenophontos, L. Oberbroeckling
ASC Report 30/2011
extended version (with slightly different title): as ASC Report 29/2011 and at arXiv:1108.2002 [math.NA]

[3] Quasi-optimal convergence rate for an adaptive boundary element method

M. Feischl, M. Karkulik, J.M. Melenk, D. Praetorius
ASC Report 28/2011

[4] A high frequency hp-boundary element method for scattering by convex polygons

D.P. Hewett, S. Langdon, J.M. Melenk
ASC Report 40/2011

[5] Mixed Conforming Elements for the Large-Body Limit in Micromagnetics: A Finite Element Approach

M. Aurada, J.M. Melenk, D. Praetorius
ASC Report 42/2011

[6] Quasi-optimal a priori estimates for fluxes in mixed finite element methods and applications to the Stokes--Darcy coupling

J.M. Melenk, H. Rezaijafari, B. Wohlmuth
ASC Report 05/2012

[7] Generalized DG-Methods for Highly Indefinite Helmholtz Problems based on the Ultra-Weak Variational Formulation

J.M. Melenk, A. Parsania, S. Sauter
ASC Report 06/2012

[8] Inverse estimates for elliptic integral operators and application to the adaptive coupling of FEM and BEM

M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
ASC Report 07/2012

[9] Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity

M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
ASC Report 08/2012

Book

Book Chapters

1. On Approximation in Meshless Methods
   in: Frontiers in Numerical Analysis, Durham 2004, J. Blowey, A. Craig (eds.), Springer Verlag 2005, pp. 65-141
   available as preprint 11/2004, department of mathematics, University of Reading ( alternative link )
2. On stability of discretizations of the Helmholtz equation
   S. Esterhazy, J.M. Melenk
   in: Numerical Analysis of Multiscale Problems, I.G. Graham, T.Y. Hou, O. Lakkis, R. Scheichl (Eds.),
   Springer LNCSE 83 (2012), pp. 285-324
   extended version available as ASC Report 01/2011 or at arXiv:1105.2112v2 [math.NA]

Refereed articles

[42] robust exponential convergence of hp-FEM for singularly perturbed reaction-diffusion systems with multiple scales

J.M. Melenk, C. Xenophontos, L. Oberbroeckling
IMA J. Numer. Anal.
available as revised version of ASC Report 31/2011

[41] mapping properties of combined field Helmholtz boundary integral operators

SIAM J. Math. Anal.
corrected version of ASC Report 01/2010

[40] Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics

S. Ferraz-Leite, J.M. Melenk, D. Praetorius
Numer. Math.
available as ASC Report 32/2011

[39] Wavenumber-explicit hp-BEM for high frequency scattering

M. Löhndorf, J.M. Melenk
SIAM J. Numer. Anal. 49 (2011), pp. 2340--2363
available as corrected version of ASC Report 02/2010

[38] Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation

J.M. Melenk, S. Sauter
SIAM J. Numer. Anal. 49 (2011), pp. 1210--1243
extended version available as corrected version of ASC Report 31/2009

[37] Runge-Kutta convolution quadrature for operators arising in wave propagation

L. Banjai, C. Lubich, J.M. Melenk
Numer. Math., 119 (2011), pp. 1-20
available as ASC Report 24/2010

[36] Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal-dual formulation and a posteriori error estimation

P. Dörsek, J.M. Melenk
Appl. Numer. Math. 60 (2010), pp. 689--704
extended version available as ASC Report 37/2009

[35] hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal formulation

P. Dörsek, J.M. Melenk
in: Spectral and high order methods for PDEs, J. Hesthaven, E. Rønquist eds, pp. 1-17, LNCSE 76, Springer Verlag (2011)
extended version available as ASC Report 36/2009

[34] Convergence Analysis for Finite Element Discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions

J.M. Melenk, S. Sauter
Math. Comp. 79 (2010), pp. 1871--1914
available as revised version of ASC Report 15/2008

[33] Optimal Convergence of Higher Order Finite Element Methods for Elliptic Interface Problems

Jingzhi Li, J.M. Melenk, Barbara Wohlmuth, Jun Zou
Appl. Numer. Math. , 60 (2010), pp. 19--37
available as revised version of ASC Report 13/2008

[32] On the suboptimality of the p-version interior penalty discontinuous Galerkin method

E. Georgoulis, E. Hall, J.M. Melenk
J. Sci. Comp. 42 (2010), pp. 54-67
available as ASC Report 03/2009

[31] On the convergence of Filon quadrature

J. Comput. Appl. Math. , 234 (2010), pp. 1692--1701

extended version available as ASC Report 08/2008

[30] p-FEM quadrature error analysis on tetrahedra

T. Eibner, J.M. Melenk, in: Proceedings of DD17, Langer, Discacciati, Keyes, Widlund, Zulehner (eds.), Springer LNSCE vol. 60 (2008), pp. 493-500 (ISSN 1439-7358)

available as ASC Report 23/2007

[29] Multilevel preconditioning for the boundary concentrated hp-FEM

T. Eibner, J.M. Melenk
Comp. Meth. Mech. Eng. 196 (2007), pp. 3713-3725

available as Preprint 05-13 of the SFB 393

[28] Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements

J. Schöberl, J.M. Melenk, C. Pechstein, S. Zaglmayr,

IMA J. Numer. Anal. 28 (2008), pp. 1-24

this article was among the top 5 downloads in 2008

available as Preprint 11/2005 of the Radon institute

[27] Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison

T. Eibner, J.M. Melenk

preprint version
in: Computer Mathematics and its Applications-Advances and Developments (1994-2005), Elias A. Lipitakis (Ed.), LEA Publ., Athens, Greece, pp. 575-596, ISBN: 960-87275-9-6

[26] An adaptive strategy for hp-FEM based on testing for analyticity

T. Eibner and J.M. Melenk

Comp. Mech. 39 (2007), pp. 575-595
preprint version

[25] a local error analysis of the boundary concentrated FEM

T. Eibner and J.M. Melenk

IMA J. Numer. Anal. 26 (2006), pp.752-778

preprint version

[24] hp-interpolation of non-smooth functions

SIAM J. Numer. Anal. 43 (2005), pp. 127-155
extended version is available as
Preprint NI03050 of the Isaac Newton Institute for Mathematical Sciences

[23] Approximation of integral operators by variable-order interpolation

S. Börm, M. Löhndorf, J.M. Melenk

Numer. Math. 99 (2005), pp. 605-643

preprint version

[22] mortar methods with curved interfaces

B. Flemisch, J.M. Melenk, B. Wohlmuth, Appl. Numer. Math. 54 (2005), pp. 339-361
preprint version

[21] Two-scale regularity for homogenization problems with non-smooth fine scale geometry

A.-M. Matache & J.M. Melenk M3AS, 13 (2003), pp. 1053-1080

available as Preprint 63 of the DFG priority program "multiscale problems"

[20] Boundary concentrated FEM

B.I. Khoromskij & J.M. Melenk, SIAM J. Numer. Anal. 41 (2003), pp. 1-36

preprint version

[19] An efficient direct solver for the boundary concentrated FEM in 2D

B.I. Khoromskij & J.M. Melenk, Computing 69 (2002), pp. 91-117

preprint version

[18] On condition numbers in hp-FEM with Gauß-Lobatto based shape functions

J. Comput. Appl. Math. , 139 (2002), pp. 21-48

preprint version (220K)

[17] On residual-based aposteriori error estimation in hp -FEM

J.M. Melenk & B. Wohlmuth, Advances in Comput. Math. , 15 (2001), pp. 311-331

preprint version (275K)

[16] Approximation orders for natural splines in arbitrary dimensions

J.M. Melenk & T. Gutzmer, Math. Comput. 70 (2001), pp. 699-703

preprint version (73K)

[15] Fully discrete hp finite elements: fast quadrature

J.M. Melenk, K. Gerdes, & C. Schwab, Comput. Meths. Appl. Mech. Engrg. 190 (2001), pp. 4339-4364

preprint version

[14] The hp-version of the Streamline Diffusion Finite Element Method in two dimensions,

K. Gerdes, J.M. Melenk, D. Schötzau, & C. Schwab, M3AS 11 (2001), pp. 301-337

abstract and paper

[13] Spectral Galerkin discretizations for hydrodynamic stability problems

J.M. Melenk, N.P. Kirchner, & C. Schwab, Computing 65 (2000), p. 97-118

abstract and paper

[12] On n-widths for elliptic problems

J. Math. Anal. Appl. 247 (2000), p. 272-289

preprint version (128K)

[11] The hp-Streamline Diffusion Method for Convection Dominated Problems in One Space Dimension

J.M. Melenk & C. Schwab, East-West J. Numer. Math. 7 (1999), 31-60

abstract and paper

[10] Operator adapted spectral element methods. I: harmonic and generalized harmonic polynomials

Numer. Math. 84 (1999), p. 35-69

preprint version

[9] An hp FEM for convection-diffusion problems in one dimension

J.M. Melenk & C. Schwab, IMA J. Numer. Anal. 19 (1999), 425-453

abstract and paper

[8] Analytic regularity for a singularly perturbed problem

J.M. Melenk & C. Schwab, SIAM J. Math. Anal., 30 (1999), 379-400

preprint version

[7] hp-FEM for Reaction-Diffusion Equations. I: Robust Exponential Convergence

J.M. Melenk & C. Schwab, SIAM J. Numer. Anal., 35 (1998), 1520-1557

preprint version

[6] On the Robust Exponential Convergence of hp-FEMs for Problems with Boundary Layers

IMA J. Numer. Anal. , 17 (1997), 577-601

abstract and paper

[5] Approximation with harmonic and generalized harmonic polynomials in the partition of unity method

J.M. Melenk & I. Babuska Comput. Assist. Mech. Eng. Sci. 4 (1997), 607-632

Load Postscript (162K)

[4] The Partition of Unity Method

I. Babuska & J.M. Melenk, Int. J. Numer. Meths. Eng., 40 (1997), 727-758

preprint version (158K)

[3] The Partition of Unity Finite Element Method: Basic Theory and Applications

J.M. Melenk & I. Babuska, Comput. Meths. Appl. Mech. Engrg.,139 (1996), 289-314

abstract and paper

[2] Finite Element Method for Solving Problems with Singular Solutions

I. Babuska, B. Andersson, B. Guo, J.M. Melenk, & H.-S. Oh, J. Comput. Appl. Math. , 74 (1996),51-70

preprint version (85K)

[1] Functions with time- and frequency-gaps

J.M. Melenk & G. Zimmermann, J. Fourier Anal. Appl. , 2 (6), 1996

preprint version (44K)

Theses

[1] hp-Finite Element Methods for Singular Perturbations

Habilitation Thesis 2000

Load Postscript (1050K)

[2] On Generalized Finite Element Methods

PhD Thesis 1995

Load Postscript (608K)

[3] Finite element methods with harmonic shape functions for solving Laplace's equation

MA Thesis 1992

Load Postscript (220K)

Selected Proceedings Contributions

[1] Mixed Conforming Elements for the Large-Body Limit in Micromagnetics

M. Aurada, J.M. Melenk, D. Praetorius
proceedings of MathMod 2009
ASC Report 49/2009

[2] Reduced Model in Thin-Film Micromagnetics

S. Ferraz-Leite, J.M. Melenk, D. Praetorius
proceedings of MathMod 2009
ASC Report 02/2009

[3] Residual a-posteriori error estimates in BEM: Convergence of h-adaptive algorithms

M. Feischl, M. Karkulik, J. Melenk, D. Praetorius:
extended abstract for IABEM 2009
ASC Report 21/2011

Unpublished Technical Reports

[1] mapping properties of Helmholtz boundary integral operators and their application to the hp-BEM

M. Löhndorf and J.M. Melenk
ASC Report 34/2009

[2] stability of the trace of the polynomial L2 projection on triangles

Bachelor thesis of T. Wurzer
ASC Report 36/2010

[3] Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs

J.M. Melenk, C. Xenophontos, L. Oberbroeckling
ASC Report 29/2011 and at arXiv:1108.2002 [math.NA]

Class Notes