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Melenk, Jens Markus

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Author ID: melenk.jens-markus Recent zbMATH articles by "Melenk, Jens Markus"
Published as: Melenk, Jens Markus; Melenk, J. M.; Melenk, Jens M.; Melenk, J. Markus; Markus Melenk, Jens

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87 Publications have been cited 2,468 times in 1,897 Documents Cited by Year
The partition of unity finite element method: basic theory and applications. Zbl 0881.65099
Melenk, J. M.; Babuška, Ivo
929
1996
The partition of unity method. Zbl 0949.65117
Babuška, I.; Melenk, J. M.
706
1997
Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation. Zbl 1229.35038
Melenk, J. M.; Sauter, S.
100
2011
On residual-based a posteriori error estimation in hp-FEM. Zbl 0991.65111
Melenk, J. M.; Wohlmuth, B. I.
94
2001
Optimal a priori estimates for higher order finite elements for elliptic interface problems. Zbl 1208.65168
Li, Jingzhi; Melenk, Jens Markus; Wohlmuth, Barbara; Zou, Jun
86
2010
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions. Zbl 1205.65301
Melenk, J. M.; Sauter, S.
78
2010
\(hp\)-interpolation of nonsmooth functions and an application to \(hp\)-a posteriori error estimation. Zbl 1087.65108
Melenk, J. M.
56
2005
\(hp\)-finite element methods for singular perturbations. Zbl 1021.65055
Melenk, Jens M.
54
2002
General DG-methods for highly indefinite Helmholtz problems. Zbl 1292.65128
Melenk, J. M.; Parsania, A.; Sauter, S.
46
2013
On stability of discretizations of the Helmholtz equation. Zbl 1248.65115
Esterhazy, S.; Melenk, J. M.
44
2012
Runge-Kutta convolution quadrature for operators arising in wave propagation. Zbl 1227.65027
Banjai, Lehel; Lubich, Christian; Melenk, Jens Markus
41
2011
Fully discrete \(hp\)-finite elements: Fast quadrature. Zbl 0985.65141
Melenk, J. M.; Gerdes, K.; Schwab, Ch.
41
2001
Quasi-optimal convergence rate for an adaptive boundary element method. Zbl 1273.65186
Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
37
2013
\(hp\) FEM for reaction-diffusion equations. I: Robust exponential convergence. Zbl 0972.65093
Melenk, Jens Markus; Schwab, Christoph
29
1998
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity. Zbl 1312.74031
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
26
2013
On the robust exponential convergence of \(hp\) finite element methods for problems with boundary layers. Zbl 0887.65106
Melenk, Jens Markus
25
1997
On condition numbers in \(hp\)-FEM with Gauss-Lobatto-based shape functions. Zbl 0997.65128
Melenk, J. M.
24
2002
Mortar methods with curved interfaces. Zbl 1078.65119
Flemisch, B.; Melenk, J. M.; Wohlmuth, B. I.
24
2005
Approximation with harmonic and generalized harmonic polynomials in the partition of unity method. Zbl 0951.65128
Melenk, J. M.; Babuška, I.
22
1997
A high frequency \(hp\) boundary element method for scattering by convex polygons. Zbl 1267.65191
Hewett, D. P.; Langdon, S.; Melenk, J. M.
20
2013
Additive Schwarz preconditioning for \(p\)-version triangular and tetrahedral finite elements. Zbl 1153.65113
Schöberl, Joachim; Melenk, Jens M.; Pechstein, Clemens; Zaglmayr, Sabine
19
2008
On approximation in meshless methods. Zbl 1082.65122
Melenk, Jens Markus
19
2005
Wavenumber-explicit \(hp\)-BEM for high frequency scattering. Zbl 1236.65149
Löhndorf, Maike; Melenk, Jens Markus
18
2011
When is the error in the \(h\)-BEM for solving the Helmholtz equation bounded independently of \(k\)? Zbl 1320.65187
Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A.
18
2015
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation. Zbl 1314.65161
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
18
2014
Local inverse estimates for non-local boundary integral operators. Zbl 1368.65242
Aurada, M.; Feischl, M.; Führer, T.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
17
2017
Operator adapted spectral element methods. I: Harmonic and generalized harmonic polynomials. Zbl 0941.65112
Melenk, J. M.
17
1999
Approximation of integral operators by variable-order interpolation. Zbl 1076.65121
Börm, Steffen; Löhndorf, Maike; Melenk, Jens M.
17
2005
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Zbl 1312.65173
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J. Markus; Praetorius, Dirk
16
2015
Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations. Zbl 1336.65148
Melenk, J. M.; Xenophontos, C.
15
2016
Analytic regularity for a singularly perturbed problem. Zbl 1023.35009
Melenk, Jens Markus; Schwab, Christoph
15
1999
Finite element method for solving problems with singular solutions. Zbl 0865.65080
Babuška, Ivo; Andersson, Börje; Guo, Benqi; Melenk, J. M.; Oh, H. S.
15
1996
On \(n\)-widths for elliptic problems. Zbl 0963.35047
Melenk, J. M.
14
2000
Boundary concentrated finite element methods. Zbl 1050.65113
Khoromskij, B. N.; Melenk, J. M.
14
2003
Adaptive \(hp\)-FEM for the contact problem with Tresca friction in linear elasticity: The primal-dual formulation and a posteriori error estimation. Zbl 1306.74036
Dörsek, P.; Melenk, J. M.
14
2010
An \(hp\) finite element method for convection-diffusion problems in one dimension. Zbl 0952.65061
Melenk, Jens Markus; Schwab, Christoph
13
1999
Tensor FEM for spectral fractional diffusion. Zbl 1429.65272
Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph
13
2019
\(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices. Zbl 1334.65192
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
12
2015
Mapping properties of combined field Helmholtz boundary integral operators. Zbl 1254.35072
Melenk, Jens Markus
12
2012
Quasi-optimal approximation of surface based Lagrange multipliers in finite element methods. Zbl 1262.65159
Melenk, J. M.; Wohlmuth, B.
12
2012
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Zbl 1375.35098
Börm, Steffen; Melenk, Jens M.
10
2017
Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales. Zbl 1278.34064
Melenk, J. M.; Xenophontos, C.; Oberbroeckling, L.
10
2013
Robust exponential convergence of \(hp\) FEM for singularly perturbed reaction-diffusion systems with multiple scales. Zbl 1328.65170
Melenk, J. M.; Xenophontos, C.; Oberbroeckling, L.
10
2013
Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation. Zbl 1361.65076
Melenk, Jens Markus; Rieder, Alexander
9
2017
On optimal \(L^2\)- and surface flux convergence in FEM. Zbl 1380.65370
Horger, T.; Melenk, J. M.; Wohlmuth, B.
9
2013
\({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian. Zbl 1435.65205
Karkulik, Michael; Melenk, Jens Markus
9
2019
Existence of \(\mathcal{H}\)-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Zbl 1327.65253
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
8
2016
On the suboptimality of the \(p\)-version interior penalty discontinuous Galerkin method. Zbl 1203.65253
Georgoulis, Emmanuil H.; Hall, Edward; Melenk, Jens Markus
8
2010
Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling. Zbl 1426.76291
Melenk, J. M.; Rezaijafari, H.; Wohlmuth, B.
7
2014
On the convergence of Filon quadrature. Zbl 1193.41032
Melenk, J. M.
7
2010
Existence of \(\mathcal{H}\)-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. Zbl 1433.65324
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
7
2017
On the stability of the boundary trace of the polynomial \(L^2\)-projection on triangles and tetrahedra. Zbl 1350.65014
Melenk, J. M.; Wurzer, T.
6
2014
Spectral Galerkin discretization for hydrodynamic stability problems. Zbl 0967.76074
Melenk, J. M.; Kirchner, N. P.; Schwab, Ch.
6
2000
Simultaneous quasi-optimal convergence rates in FEM-BEM coupling. Zbl 1359.65263
Melenk, J. M.; Praetorius, D.; Wohlmuth, B.
6
2017
An analysis of discretizations of the Helmholtz equation in \(L^2\) and in negative norms. Zbl 1350.65123
Esterhazy, S.; Melenk, J. M.
5
2014
An \(hp\)-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems. Zbl 1360.49019
Amrein, Mario; Melenk, Jens Markus; Wihler, Thomas P.
5
2017
Functions with time and frequency gaps. Zbl 0913.42007
Melenk, Jens M.; Zimmermann, Georg
5
1996
The \(hp\)-version of the streamline diffusion finite element method in two space dimensions. Zbl 1012.65122
Gerdes, K.; Melenk, J. M.; Schwab, Christoph; Schötzau, Dominik
5
2001
The \(hp\) streamline diffusion finite element method for convection dominated problems in one space dimension. Zbl 0920.65047
Melenk, Jens Markus; Schwab, Christoph
5
1999
Local high-order regularization and applications to \(hp\)-methods. Zbl 1443.65349
Karkulik, M.; Melenk, J. M.
5
2015
On commuting \(p\)-version projection-based interpolation on tetrahedra. Zbl 1426.65181
Melenk, J. M.; Rojik, C.
5
2020
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. Zbl 07283112
Mascotto, Lorenzo; Melenk, Jens M.; Perugia, Ilaria; Rieder, Alexander
5
2020
An efficient direct solver for the boundary concentrated FEM in 2D. Zbl 1017.65089
Khoromskij, B. N.; Melenk, J. M.
4
2002
\(hp\)-FEM for the fractional heat equation. Zbl 1466.65141
Markus Melenk, Jens; Rieder, Alexander
4
2021
Two-scale regularity for homogenization problems with nonsmooth fine scale geometry. Zbl 1076.35505
Matache, A.-M.; Melenk, J. M.
3
2003
Symmetry-free, \(p\)-robust equilibrated error indication for the \(hp\)-version of the FEM in nearly incompressible linear elasticity. Zbl 1357.74060
Dörsek, Philipp; Melenk, Jens M.
3
2013
FEM-BEM coupling for the large-body limit in micromagnetics. Zbl 1310.78014
Aurada, M.; Melenk, J. M.; Praetorius, D.
3
2015
Approximating inverse FEM matrices on non-uniform meshes with \(\mathcal{H}\)-matrices. Zbl 1472.65051
Angleitner, Niklas; Faustmann, Markus; Melenk, Jens Markus
3
2021
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Zbl 1263.78017
Ferraz-Leite, Samuel; Melenk, Jens Markus; Praetorius, Dirk
3
2012
Wavenumber-explicit hp-FEM analysis for Maxwell’s equations with transparent boundary conditions. Zbl 1460.35085
Melenk, Jens M.; Sauter, Stefan A.
3
2021
Mixed conforming elements for the large-body limit in micromagnetics. Zbl 1285.65076
Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
A new proof for existence of \(\mathcal H\)-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. Zbl 1282.65153
Faustmann, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Zbl 1478.65121
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
2
2021
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion. Zbl 07381649
Faustmann, Markus; Melenk, Jens Markus; Parvizi, Maryam
2
2021
\(hp\)-FEM for the contact problem with Tresca friction in linear elasticity: the primal formulation. Zbl 1417.74019
Dörsek, P.; Melenk, J. M.
2
2011
Local convergence of the boundary element method on polyhedral domains. Zbl 1402.65173
Faustmann, Markus; Melenk, Jens Markus
2
2018
An analysis of a butterfly algorithm. Zbl 1396.65171
Börm, S.; Börst, C.; Melenk, J. M.
2
2017
Approximation orders for natural splines in arbitrary dimensions. Zbl 0967.41009
Gutzmer, Tim; Melenk, Jens Markus
1
2001
Analysis of the \(hp\)-version of a first order system least squares method for the Helmholtz equation. Zbl 1433.65276
Bernkopf, Maximilian; Melenk, Jens Markus
1
2019
Direct and inverse problems in wave propagation and applications. Selected papers of the workshop on wave propagation and scattering, inverse problems and applications in energy and the environment, Linz, Austria, November 21–25, 2011. Zbl 1272.78001
1
2013
Stable decompositions of \(hp\)-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D. Zbl 07201580
Karkulik, Michael; Melenk, Jens Markus; Rieder, Alexander
1
2020
On superconvergence of Runge-Kutta convolution quadrature for the wave equation. Zbl 1467.65091
Melenk, Jens Markus; Rieder, Alexander
1
2021
Runge-Kutta approximation for \(C_0\)-semigroups in the graph norm with applications to time domain boundary integral equations. Zbl 1473.65085
Rieder, Alexander; Sayas, Francisco-Javier; Melenk, Jens Markus
1
2020
Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains. Zbl 1397.65264
Faustmann, M.; Melenk, J. M.
1
2017
Metastable speeds in the fractional Allen-Cahn equation. Zbl 07424212
Achleitner, Franz; Kuehn, Christian; Melenk, Jens M.; Rieder, Alexander
1
2021
Caccioppoli-type estimates and \(\mathcal{H}\)-matrix approximations to inverses for FEM-BEM couplings. Zbl 07501301
Faustmann, Markus; Melenk, Jens Markus; Parvizi, Maryam
1
2022
Mortar coupling of \(hp\)-discontinuous Galerkin and boundary element methods for the Helmholtz equation. Zbl 1492.65304
Erath, Christoph; Mascotto, Lorenzo; Melenk, Jens M.; Perugia, Ilaria; Rieder, Alexander
1
2022
Caccioppoli-type estimates and \(\mathcal{H}\)-matrix approximations to inverses for FEM-BEM couplings. Zbl 07501301
Faustmann, Markus; Melenk, Jens Markus; Parvizi, Maryam
1
2022
Mortar coupling of \(hp\)-discontinuous Galerkin and boundary element methods for the Helmholtz equation. Zbl 1492.65304
Erath, Christoph; Mascotto, Lorenzo; Melenk, Jens M.; Perugia, Ilaria; Rieder, Alexander
1
2022
\(hp\)-FEM for the fractional heat equation. Zbl 1466.65141
Markus Melenk, Jens; Rieder, Alexander
4
2021
Approximating inverse FEM matrices on non-uniform meshes with \(\mathcal{H}\)-matrices. Zbl 1472.65051
Angleitner, Niklas; Faustmann, Markus; Melenk, Jens Markus
3
2021
Wavenumber-explicit hp-FEM analysis for Maxwell’s equations with transparent boundary conditions. Zbl 1460.35085
Melenk, Jens M.; Sauter, Stefan A.
3
2021
Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian. Zbl 1478.65121
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
2
2021
On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion. Zbl 07381649
Faustmann, Markus; Melenk, Jens Markus; Parvizi, Maryam
2
2021
On superconvergence of Runge-Kutta convolution quadrature for the wave equation. Zbl 1467.65091
Melenk, Jens Markus; Rieder, Alexander
1
2021
Metastable speeds in the fractional Allen-Cahn equation. Zbl 07424212
Achleitner, Franz; Kuehn, Christian; Melenk, Jens M.; Rieder, Alexander
1
2021
On commuting \(p\)-version projection-based interpolation on tetrahedra. Zbl 1426.65181
Melenk, J. M.; Rojik, C.
5
2020
FEM-BEM mortar coupling for the Helmholtz problem in three dimensions. Zbl 07283112
Mascotto, Lorenzo; Melenk, Jens M.; Perugia, Ilaria; Rieder, Alexander
5
2020
Stable decompositions of \(hp\)-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D. Zbl 07201580
Karkulik, Michael; Melenk, Jens Markus; Rieder, Alexander
1
2020
Runge-Kutta approximation for \(C_0\)-semigroups in the graph norm with applications to time domain boundary integral equations. Zbl 1473.65085
Rieder, Alexander; Sayas, Francisco-Javier; Melenk, Jens Markus
1
2020
Tensor FEM for spectral fractional diffusion. Zbl 1429.65272
Banjai, Lehel; Melenk, Jens M.; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.; Schwab, Christoph
13
2019
\({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian. Zbl 1435.65205
Karkulik, Michael; Melenk, Jens Markus
9
2019
Analysis of the \(hp\)-version of a first order system least squares method for the Helmholtz equation. Zbl 1433.65276
Bernkopf, Maximilian; Melenk, Jens Markus
1
2019
Local convergence of the boundary element method on polyhedral domains. Zbl 1402.65173
Faustmann, Markus; Melenk, Jens Markus
2
2018
Local inverse estimates for non-local boundary integral operators. Zbl 1368.65242
Aurada, M.; Feischl, M.; Führer, T.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
17
2017
Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis. Zbl 1375.35098
Börm, Steffen; Melenk, Jens M.
10
2017
Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation. Zbl 1361.65076
Melenk, Jens Markus; Rieder, Alexander
9
2017
Existence of \(\mathcal{H}\)-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. Zbl 1433.65324
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
7
2017
Simultaneous quasi-optimal convergence rates in FEM-BEM coupling. Zbl 1359.65263
Melenk, J. M.; Praetorius, D.; Wohlmuth, B.
6
2017
An \(hp\)-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems. Zbl 1360.49019
Amrein, Mario; Melenk, Jens Markus; Wihler, Thomas P.
5
2017
An analysis of a butterfly algorithm. Zbl 1396.65171
Börm, S.; Börst, C.; Melenk, J. M.
2
2017
Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains. Zbl 1397.65264
Faustmann, M.; Melenk, J. M.
1
2017
Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations. Zbl 1336.65148
Melenk, J. M.; Xenophontos, C.
15
2016
Existence of \(\mathcal{H}\)-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Zbl 1327.65253
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
8
2016
When is the error in the \(h\)-BEM for solving the Helmholtz equation bounded independently of \(k\)? Zbl 1320.65187
Graham, I. G.; Löhndorf, M.; Melenk, J. M.; Spence, E. A.
18
2015
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. II: Hyper-singular integral equation. Zbl 1312.65173
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, J. Markus; Praetorius, Dirk
16
2015
\(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices. Zbl 1334.65192
Faustmann, Markus; Melenk, Jens Markus; Praetorius, Dirk
12
2015
Local high-order regularization and applications to \(hp\)-methods. Zbl 1443.65349
Karkulik, M.; Melenk, J. M.
5
2015
FEM-BEM coupling for the large-body limit in micromagnetics. Zbl 1310.78014
Aurada, M.; Melenk, J. M.; Praetorius, D.
3
2015
Quasi-optimal convergence rates for adaptive boundary element methods with data approximation. I: Weakly-singular integral equation. Zbl 1314.65161
Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
18
2014
Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling. Zbl 1426.76291
Melenk, J. M.; Rezaijafari, H.; Wohlmuth, B.
7
2014
On the stability of the boundary trace of the polynomial \(L^2\)-projection on triangles and tetrahedra. Zbl 1350.65014
Melenk, J. M.; Wurzer, T.
6
2014
An analysis of discretizations of the Helmholtz equation in \(L^2\) and in negative norms. Zbl 1350.65123
Esterhazy, S.; Melenk, J. M.
5
2014
Mixed conforming elements for the large-body limit in micromagnetics. Zbl 1285.65076
Aurada, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
A new proof for existence of \(\mathcal H\)-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. Zbl 1282.65153
Faustmann, Markus; Melenk, Jens M.; Praetorius, Dirk
2
2014
General DG-methods for highly indefinite Helmholtz problems. Zbl 1292.65128
Melenk, J. M.; Parsania, A.; Sauter, S.
46
2013
Quasi-optimal convergence rate for an adaptive boundary element method. Zbl 1273.65186
Feischl, M.; Karkulik, M.; Melenk, J. M.; Praetorius, D.
37
2013
Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity. Zbl 1312.74031
Aurada, Markus; Feischl, Michael; Führer, Thomas; Karkulik, Michael; Melenk, Jens Markus; Praetorius, Dirk
26
2013
A high frequency \(hp\) boundary element method for scattering by convex polygons. Zbl 1267.65191
Hewett, D. P.; Langdon, S.; Melenk, J. M.
20
2013
Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales. Zbl 1278.34064
Melenk, J. M.; Xenophontos, C.; Oberbroeckling, L.
10
2013
Robust exponential convergence of \(hp\) FEM for singularly perturbed reaction-diffusion systems with multiple scales. Zbl 1328.65170
Melenk, J. M.; Xenophontos, C.; Oberbroeckling, L.
10
2013
On optimal \(L^2\)- and surface flux convergence in FEM. Zbl 1380.65370
Horger, T.; Melenk, J. M.; Wohlmuth, B.
9
2013
Symmetry-free, \(p\)-robust equilibrated error indication for the \(hp\)-version of the FEM in nearly incompressible linear elasticity. Zbl 1357.74060
Dörsek, Philipp; Melenk, Jens M.
3
2013
Direct and inverse problems in wave propagation and applications. Selected papers of the workshop on wave propagation and scattering, inverse problems and applications in energy and the environment, Linz, Austria, November 21–25, 2011. Zbl 1272.78001
1
2013
On stability of discretizations of the Helmholtz equation. Zbl 1248.65115
Esterhazy, S.; Melenk, J. M.
44
2012
Mapping properties of combined field Helmholtz boundary integral operators. Zbl 1254.35072
Melenk, Jens Markus
12
2012
Quasi-optimal approximation of surface based Lagrange multipliers in finite element methods. Zbl 1262.65159
Melenk, J. M.; Wohlmuth, B.
12
2012
Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics. Zbl 1263.78017
Ferraz-Leite, Samuel; Melenk, Jens Markus; Praetorius, Dirk
3
2012
Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation. Zbl 1229.35038
Melenk, J. M.; Sauter, S.
100
2011
Runge-Kutta convolution quadrature for operators arising in wave propagation. Zbl 1227.65027
Banjai, Lehel; Lubich, Christian; Melenk, Jens Markus
41
2011
Wavenumber-explicit \(hp\)-BEM for high frequency scattering. Zbl 1236.65149
Löhndorf, Maike; Melenk, Jens Markus
18
2011
\(hp\)-FEM for the contact problem with Tresca friction in linear elasticity: the primal formulation. Zbl 1417.74019
Dörsek, P.; Melenk, J. M.
2
2011
Optimal a priori estimates for higher order finite elements for elliptic interface problems. Zbl 1208.65168
Li, Jingzhi; Melenk, Jens Markus; Wohlmuth, Barbara; Zou, Jun
86
2010
Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions. Zbl 1205.65301
Melenk, J. M.; Sauter, S.
78
2010
Adaptive \(hp\)-FEM for the contact problem with Tresca friction in linear elasticity: The primal-dual formulation and a posteriori error estimation. Zbl 1306.74036
Dörsek, P.; Melenk, J. M.
14
2010
On the suboptimality of the \(p\)-version interior penalty discontinuous Galerkin method. Zbl 1203.65253
Georgoulis, Emmanuil H.; Hall, Edward; Melenk, Jens Markus
8
2010
On the convergence of Filon quadrature. Zbl 1193.41032
Melenk, J. M.
7
2010
Additive Schwarz preconditioning for \(p\)-version triangular and tetrahedral finite elements. Zbl 1153.65113
Schöberl, Joachim; Melenk, Jens M.; Pechstein, Clemens; Zaglmayr, Sabine
19
2008
\(hp\)-interpolation of nonsmooth functions and an application to \(hp\)-a posteriori error estimation. Zbl 1087.65108
Melenk, J. M.
56
2005
Mortar methods with curved interfaces. Zbl 1078.65119
Flemisch, B.; Melenk, J. M.; Wohlmuth, B. I.
24
2005
On approximation in meshless methods. Zbl 1082.65122
Melenk, Jens Markus
19
2005
Approximation of integral operators by variable-order interpolation. Zbl 1076.65121
Börm, Steffen; Löhndorf, Maike; Melenk, Jens M.
17
2005
Boundary concentrated finite element methods. Zbl 1050.65113
Khoromskij, B. N.; Melenk, J. M.
14
2003
Two-scale regularity for homogenization problems with nonsmooth fine scale geometry. Zbl 1076.35505
Matache, A.-M.; Melenk, J. M.
3
2003
\(hp\)-finite element methods for singular perturbations. Zbl 1021.65055
Melenk, Jens M.
54
2002
On condition numbers in \(hp\)-FEM with Gauss-Lobatto-based shape functions. Zbl 0997.65128
Melenk, J. M.
24
2002
An efficient direct solver for the boundary concentrated FEM in 2D. Zbl 1017.65089
Khoromskij, B. N.; Melenk, J. M.
4
2002
On residual-based a posteriori error estimation in hp-FEM. Zbl 0991.65111
Melenk, J. M.; Wohlmuth, B. I.
94
2001
Fully discrete \(hp\)-finite elements: Fast quadrature. Zbl 0985.65141
Melenk, J. M.; Gerdes, K.; Schwab, Ch.
41
2001
The \(hp\)-version of the streamline diffusion finite element method in two space dimensions. Zbl 1012.65122
Gerdes, K.; Melenk, J. M.; Schwab, Christoph; Schötzau, Dominik
5
2001
Approximation orders for natural splines in arbitrary dimensions. Zbl 0967.41009
Gutzmer, Tim; Melenk, Jens Markus
1
2001
On \(n\)-widths for elliptic problems. Zbl 0963.35047
Melenk, J. M.
14
2000
Spectral Galerkin discretization for hydrodynamic stability problems. Zbl 0967.76074
Melenk, J. M.; Kirchner, N. P.; Schwab, Ch.
6
2000
Operator adapted spectral element methods. I: Harmonic and generalized harmonic polynomials. Zbl 0941.65112
Melenk, J. M.
17
1999
Analytic regularity for a singularly perturbed problem. Zbl 1023.35009
Melenk, Jens Markus; Schwab, Christoph
15
1999
An \(hp\) finite element method for convection-diffusion problems in one dimension. Zbl 0952.65061
Melenk, Jens Markus; Schwab, Christoph
13
1999
The \(hp\) streamline diffusion finite element method for convection dominated problems in one space dimension. Zbl 0920.65047
Melenk, Jens Markus; Schwab, Christoph
5
1999
\(hp\) FEM for reaction-diffusion equations. I: Robust exponential convergence. Zbl 0972.65093
Melenk, Jens Markus; Schwab, Christoph
29
1998
The partition of unity method. Zbl 0949.65117
Babuška, I.; Melenk, J. M.
706
1997
On the robust exponential convergence of \(hp\) finite element methods for problems with boundary layers. Zbl 0887.65106
Melenk, Jens Markus
25
1997
Approximation with harmonic and generalized harmonic polynomials in the partition of unity method. Zbl 0951.65128
Melenk, J. M.; Babuška, I.
22
1997
The partition of unity finite element method: basic theory and applications. Zbl 0881.65099
Melenk, J. M.; Babuška, Ivo
929
1996
Finite element method for solving problems with singular solutions. Zbl 0865.65080
Babuška, Ivo; Andersson, Börje; Guo, Benqi; Melenk, J. M.; Oh, H. S.
15
1996
Functions with time and frequency gaps. Zbl 0913.42007
Melenk, Jens M.; Zimmermann, Georg
5
1996
all top 5

Cited by 2,626 Authors

37 Melenk, Jens Markus
34 Praetorius, Dirk
31 Babuška, Ivo
31 Belytschko, Ted Bohdan
25 Trevelyan, Jon
25 Zheng, Hong
22 Bordas, Stéphane Pierre Alain
21 Sukumar, Natarajan
20 Moës, Nicolas
19 Laghrouche, Omar
18 Yang, Yongtao
17 Feischl, Michael
17 Führer, Thomas
16 Duarte, Carlos Armando
16 Rabczuk, Timon
15 Banerjee, Uday
15 Farhat, Charbel H.
15 Karkulik, Michael
15 Liu, Gui-Rong
15 Perugia, Ilaria
15 Sauter, Stefan A.
15 Schwab, Christoph
15 Sluys, Lambertus Johannes
15 Spence, Euan A.
15 Xenophontos, Christos A.
14 Cavoretto, Roberto
14 Dehghan Takht Fooladi, Mehdi
14 Hiptmair, Ralf
14 Wohlmuth, Barbara I.
13 Chen, Jiun-Shyan
13 Dolbow, John E.
13 Mohamed, M. Shadi
12 Bettess, Peter
12 De Rossi, Alessandra
12 Liu, Wing Kam
12 Oh, Hae-Soo
12 Shivanian, Elyas
11 Gravouil, Anthony
11 Harari, Isaac
11 Sayas, Francisco-Javier
11 Schroder, Andreas
11 Seaïd, Mohammed
11 Soghrati, Soheil
11 Wihler, Thomas Pascal
10 Barros, Felício Bruzzi
10 Börm, Steffen
10 Faustmann, Markus
10 Houston, Paul
10 Mascotto, Lorenzo
10 Rieder, Alexander
10 Schweitzer, Marc Alexander
10 Tezaur, Radek
9 Chung, Tsz Shun Eric
9 Cueto, Elias
9 Doblaré, Manuel
9 Monk, Peter B.
9 Natarajan, Sundararajan
9 Stephan, Ernst Peter
8 Avazzadeh, Zakieh
8 Banz, Lothar
8 Davis, Christopher B.
8 Gavete, Luis
8 Geubelle, Philippe H.
8 Giani, Stefano
8 Guo, Ruchi
8 Ladevèze, Pierre
8 Lin, Tao
8 Nikan, Omid
8 Perracchione, Emma
8 Perrey-Debain, Emmanuel
8 Salehi, Rezvan
8 Schötzau, Dominik
8 Tang, Xuhai
8 Tian, Rong
8 Wang, Lihua
8 Zhang, Qinghui
8 Zhang, Zhimin
7 Baietto, Marie-Christine
7 Benvenuti, Elena
7 Bouillard, Philippe
7 Chen, Yanping
7 de Borst, René
7 El Kacimi, Abdellah
7 Fries, Thomas-Peter
7 Fu, Shubin
7 Graham, Ivan G.
7 Heuer, Norbert
7 Hou, Yanren
7 Ji, Haifeng
7 Khoei, Amir R.
7 Legrain, Gregory
7 Machado, Roberto Dalledone
7 Moiola, Andrea
7 Nochetto, Ricardo Horacio
7 Shu, Chang
7 Strouboulis, Theofanis
7 Youn, Sung-Kie
7 Zhou, Jianwei
6 Banjai, Lehel
6 Betcke, Timo
...and 2,526 more Authors
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Cited in 164 Serials

394 Computer Methods in Applied Mechanics and Engineering
199 International Journal for Numerical Methods in Engineering
119 Engineering Analysis with Boundary Elements
105 Computational Mechanics
79 Journal of Computational Physics
70 Computers & Mathematics with Applications
63 Numerische Mathematik
57 Journal of Computational and Applied Mathematics
49 Applied Numerical Mathematics
37 Journal of Scientific Computing
35 SIAM Journal on Scientific Computing
34 Mathematics of Computation
34 Applied Mathematical Modelling
33 International Journal of Computational Methods
31 SIAM Journal on Numerical Analysis
28 Applied Mathematics and Computation
23 Communications in Numerical Methods in Engineering
19 Advances in Computational Mathematics
19 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
18 Numerical Methods for Partial Differential Equations
17 Archives of Computational Methods in Engineering
14 Calcolo
14 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
13 Computational Methods in Applied Mathematics
12 European Journal of Mechanics. A. Solids
11 Acta Mechanica
10 Numerical Algorithms
10 Mathematical Problems in Engineering
10 International Journal of Fracture
9 Computers and Fluids
8 Journal of the Mechanics and Physics of Solids
8 COMPEL
7 Wave Motion
7 Computing
7 International Journal of Computer Mathematics
7 Engineering Computations
7 Journal of Numerical Mathematics
7 Multiscale Modeling & Simulation
7 Journal of Computational Acoustics
6 International Journal of Solids and Structures
6 Mathematical Methods in the Applied Sciences
6 Mathematics and Computers in Simulation
6 Applied Mathematics and Mechanics. (English Edition)
6 Applied Mathematics Letters
6 Computational and Applied Mathematics
6 Computing and Visualization in Science
6 Communications in Computational Physics
5 BIT
5 International Journal of Numerical Analysis and Modeling
4 Applicable Analysis
4 Journal of Mathematical Analysis and Applications
4 Integral Equations and Operator Theory
4 Archive of Applied Mechanics
4 Foundations of Computational Mathematics
3 International Journal of Engineering Science
3 Journal of Engineering Mathematics
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Applications of Mathematics
3 Computational Geosciences
3 Discrete and Continuous Dynamical Systems. Series B
3 Sādhanā
3 International Journal for Computational Methods in Engineering Science and Mechanics
3 Algorithms
3 Advances in Applied Mathematics and Mechanics
3 International Journal for Numerical Methods in Biomedical Engineering
2 Archive for Rational Mechanics and Analysis
2 Computer Physics Communications
2 International Journal for Numerical and Analytical Methods in Geomechanics
2 Journal of Fluid Mechanics
2 Journal of Approximation Theory
2 SIAM Journal on Control and Optimization
2 Journal of Integral Equations and Applications
2 SIAM Journal on Mathematical Analysis
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 International Journal of Numerical Methods for Heat & Fluid Flow
2 Discrete and Continuous Dynamical Systems
2 Abstract and Applied Analysis
2 Acta Numerica
2 Advances in Difference Equations
2 Acta Mechanica Sinica
2 Science China. Mathematics
2 S\(\vec{\text{e}}\)MA Journal
2 ISRN Applied Mathematics
2 Computational Methods for Differential Equations
2 International Journal of Applied and Computational Mathematics
2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2 Communications on Applied Mathematics and Computation
2 SN Partial Differential Equations and Applications
1 Communications on Pure and Applied Mathematics
1 International Journal for Numerical Methods in Fluids
1 Nonlinearity
1 Studia Mathematica
1 Bulletin of Mathematical Biology
1 Theoretical and Computational Fluid Dynamics
1 Chaos, Solitons and Fractals
1 ACM Transactions on Mathematical Software
1 Kybernetika
1 Mathematische Nachrichten
1 Meccanica
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
...and 64 more Serials
all top 5

Cited in 37 Fields

1,280 Numerical analysis (65-XX)
817 Mechanics of deformable solids (74-XX)
505 Partial differential equations (35-XX)
326 Fluid mechanics (76-XX)
81 Optics, electromagnetic theory (78-XX)
42 Classical thermodynamics, heat transfer (80-XX)
40 Calculus of variations and optimal control; optimization (49-XX)
39 Approximations and expansions (41-XX)
28 Biology and other natural sciences (92-XX)
27 Ordinary differential equations (34-XX)
16 Real functions (26-XX)
15 Integral equations (45-XX)
15 Statistical mechanics, structure of matter (82-XX)
14 Functional analysis (46-XX)
14 Geophysics (86-XX)
11 Operator theory (47-XX)
11 Probability theory and stochastic processes (60-XX)
11 Computer science (68-XX)
8 Operations research, mathematical programming (90-XX)
7 Potential theory (31-XX)
7 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
7 Systems theory; control (93-XX)
6 Global analysis, analysis on manifolds (58-XX)
6 Statistics (62-XX)
5 Linear and multilinear algebra; matrix theory (15-XX)
5 Dynamical systems and ergodic theory (37-XX)
5 Harmonic analysis on Euclidean spaces (42-XX)
5 Quantum theory (81-XX)
3 Mechanics of particles and systems (70-XX)
2 Combinatorics (05-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 Mathematical logic and foundations (03-XX)
1 Number theory (11-XX)
1 Difference and functional equations (39-XX)
1 Integral transforms, operational calculus (44-XX)
1 Differential geometry (53-XX)

Citations by Year