Publications of Norbert Heuer

Preprints/submitted manuscripts

• A fractional-order trace-dev-div inequality (with C. Carstensen)
  abstract, arXiv:2403.01291
• Generalized mixed and primal hybrid methods with applications to plate bending
  abstract, arXiv:2406.12541

In journals

• Normal-normal continuous symmetric stresses in mixed finite element elasticity (with C. Carstensen)
  Math. Comp. (appeared online)
  abstract, journal page
• Mixed finite elements for Kirchhoff–Love plate bending (with T. Führer)
  Math. Comp. (appeared online)
  abstract, arXiv:2305.08693, journal page
• Stability analysis for acoustic waveguides. Part 3: Impedance boundary conditions (with L. Demkowicz and J. Gopalakrishnan)
  Appl. Math. 69 (5), 633–651, 2024.
  abstract, Oden Institute Report 24-01, journal page
• A balanced finite-element method for an axisymmetrically loaded thin shell (with T. Linß)
  Appl. Math. 69 (2), 151–168, 2024.
  abstract, arXiv:2306.12952, journal page
• Robust DPG test spaces and Fortin operators — the H¹ and H(div) cases (with T. Führer)
  SIAM J. Numer. Anal. 62 (2), 718–748, 2024.
  abstract, arXiv:2301.13021, journal page
• A DPG method for the quad-curl problem (with T. Führer and P. Herrera)
  Comput. Math. Appl. 149, 221–238, 2023.
  abstract, arXiv:2301.10588, journal page
• A DPG method for Reissner–Mindlin plates (with T. Führer and A. H. Niemi)
  SIAM J. Numer. Anal. 61 (2), 995–1017, 2023.
  abstract, arXiv:2205.13301, journal page
• A DPG method for shallow shells (with T. Führer and A. H. Niemi)
  Numer. Math. 152 (1), 67–99, 2022.
  abstract, arXiv:2107.07624, journal page
• DPG methods for a fourth-order div problem (with T. Führer and P. Herrera)
  Comput. Methods Appl. Math., 22 (3), 545–562, 2022.
  abstract, arXiv:2112.15153, journal page
• MINRES for second-order PDEs with singular data (with T. Führer and M. Karkulik)
  SIAM J. Numer. Anal., 60 (3), 1111–1135, 2022.
  abstract, arXiv:2111.00103, journal page
• Analysis of backward Euler primal DPG methods (with T. Führer and M. Karkulik)
  Comput. Methods Appl. Math. 21 (4), 811–826, 2021.
  abstract, arXiv:2103.12181, journal page
• The double adaptivity paradigm (with L. Demkowicz, T. Führer, and X. Tian)
  Comput. Math. Appl. 95, 41–66, 2021.
  abstract, ICES Report 19-07, journal page
• A robust DPG method for large domains (with T. Führer)
  Comput. Math. Appl. 94, 15–27, 2021.
  abstract, arXiv:2011.12098, journal page
• Trace operators of the bi-Laplacian and applications (with T. Führer and A. Haberl)
  IMA J. Numer. Anal. 41 (2), 1031–1055, 2021.
  abstract, arXiv:1904.07761, journal page
• A locking-free DPG scheme for Timoshenko beams (with T. Führer and C. García Vera)
  Comput. Methods Appl. Math. 21 (2), 373–383, 2021.
  abstract, arXiv:2004.00455, journal page
• An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation (with T. Führer and F.–J. Sayas)
  Numer. Math. 145 (2), 313–344, 2020.
  abstract, arXiv:1906.04869, journal page
• Finite element approximations of the nonhomogeneous fractional Dirichlet problem (with G. Acosta and J. P. Borthagaray)
  IMA J. Numer. Anal. 39 (3), 1471–1501, 2019.
  abstract, arXiv:1709.06592, journal page
• Optimal quasi-diagonal preconditioners for pseudodifferential operators of order minus two (with T. Führer)
  J. Sci. Comput. 79, 1161–1181, 2019.
  abstract, arXiv:1806.07933, journal page
• Fully discrete DPG methods for the Kirchhoff–Love plate bending model (with T. Führer)
  Comput. Methods Appl. Mech. Engrg. 343, 550–571, 2019.
  abstract, arXiv:1805.08864, journal page
• An ultraweak formulation of the Kirchhoff–Love plate bending model and DPG approximation (with T. Führer and A. H. Niemi)
  Math. Comp. 88 (318), 1587–1619, 2019.
  abstract, arXiv:1805.07835, journal page
• A DPG framework for strongly monotone operators (with P. Cantin)
  SIAM J. Numer. Anal. 56 (5), 2731–2750, 2018.
  abstract, hal-01690281v1, journal page
• On the DPG method for Signorini problems (with T. Führer and E. P. Stephan)
  IMA J. Numer. Anal. 38 (4), 1893–1926, 2018.
  abstract, arXiv:1609.00765, journal page (public access)
• Combining the DPG method with finite elements (with T. Führer, M. Karkulik and R. Rodríguez)
  Comput. Methods Appl. Math. 18 (4), 639–652, 2018.
  abstract, arXiv:1704.07471, journal page
• Regularity of the solution to 1-D fractional order diffusion equations (with V. J. Ervin and J. P. Roop)
  Math. Comp. 87 (313), 2273–2294, 2018.
  abstract, arXiv:1608.00128, journal page
• A wirebasket preconditioner for the mortar boundary element method (with T. Führer)
  Adv. Comput. Math. 44 (1), 23–49, 2018.
  abstract, arXiv:1506.00701, journal page
• A non-symmetric coupling of boundary elements with the hybridizable discontinuous Galerkin method (with Z. Fu and F.–J. Sayas)
  Comput. Math. Appl. 74 (11), 2752–2768, 2017.
  abstract, arXiv:1212.2128, journal page
• Robust coupling of DPG and BEM for a singularly perturbed transmission problem (with T. Führer)
  Comput. Math. Appl. 74 (8), 1940–1954, 2017.
  abstract, arXiv:1603.05164, journal page
• DPG method with optimal test functions for a fractional advection diffusion equation (with V. J. Ervin, T. Führer, and M. Karkulik)
  J. Sci. Comput. 72 (2), 568–585, 2017.
  abstract, arXiv:1507.06691, journal page
• A robust DPG method for singularly perturbed reaction-diffusion problems (with M. Karkulik)
  SIAM J. Numer. Anal. 55 (3), 1218–1242, 2017.
  abstract, arXiv:1509.07560, journal page
• On the coupling of DPG and BEM (with T. Führer and M. Karkulik)
  Math. Comp. 86 (307), 2261–2284, 2017.
  abstract, arXiv:1508.00630, journal page
• A time-stepping DPG scheme for the heat equation (with T. Führer and J. Sen Gupta)
  Comput. Methods Appl. Math. 17 (2), 237–252, 2017.
  abstract, arXiv:1607.00301, journal page
• Discontinuous Petrov–Galerkin boundary elements (with M. Karkulik)
  Numer. Math. 135 (4), 1011–1043, 2017.
  abstract, arXiv:1408.5374, journal page
• A non-conforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator (with G. Salmerón)
  Numer. Methods Partial Differential Eq. 33 (1), 125–141, 2017.
  abstract, arXiv:1506.00688, journal page
• Symmetric coupling of LDG-FEM and DG-BEM (with S. Meddahi and F.–J. Sayas)
  J. Sci. Comput. 68 (1), 303–325, 2016.
  abstract, arXiv:1310.3201, journal page
• DPG method with optimal test functions for a transmission problem (with M. Karkulik)
  Comput. Math. Appl. 70 (5), 1504–1518, 2015.
  abstract, arXiv:1412.4753, journal page
• Adaptive boundary element methods (with M. Feischl, T. Führer, M. Karkulik, and D. Praetorius)
  Arch. Comput. Methods Eng. 22 (3), 309–389, 2015.
  abstract, arXiv:1402.0744, journal page
• Adaptive Crouzeix–Raviart boundary element method (with M. Karkulik)
  ESAIM Math. Model. Num. Anal. 49 (4), 1193–1217, 2015.
  abstract, arXiv:1312.0484, journal page
• Analysis of a non-symmetric coupling of Interior Penalty DG and BEM (with F.–J. Sayas)
  Math. Comp. 84 (292), 581–598, 2015.
  abstract, arXiv:1111.2344, journal page
• Note on discontinuous trace approximation in the practical DPG method (with M. Karkulik and F.–J. Sayas)
  Comput. Math. Appl. 68, 1562–1568, 2014.
  abstract, arXiv:1402.5169, journal page
• Ultra-weak formulation of a hypersingular integral equation on polygons and DPG method with optimal test functions (with F. Pinochet)
  SIAM J. Numer. Anal. 52 (6), 2703–2721, 2014.
  abstract, arXiv:1309.1697, journal page
• Coupling of mixed finite element and stabilized boundary element methods for a fluid-solid interaction problem in 3D (with G. N. Gatica and S. Meddahi)
  Numer. Methods Partial Differential Eq. 30 (4), 1211–1233, 2014.
  abstract, preprint, journal page
• A posteriori error analysis for a boundary element method with non-conforming domain decomposition (with C. Domínguez)
  Numer. Methods Partial Differential Eq. 30 (3), 947–963, 2014.
  abstract, arXiv:1307.7310, journal page
• On the equivalence of fractional-order Sobolev semi-norms
  J. Math. Anal. Appl. 417 (2), 505–518, 2014.
  abstract, arXiv:1211.0340, journal page
• Robust DPG method for convection-dominated diffusion problems II: Adjoint boundary conditions and mesh-dependent test norms (with J. Chan, T. Bui–Thanh, and L. F. Demkowicz)
  Comput. Math. Appl. 67 (4), 771–795, 2014.
  abstract, ICES Report 12-21, journal page
• Discontinuous Galerkin hp-BEM with quasi-uniform meshes (with S. Meddahi)
  Numer. Math. 125 (4), 679–703, 2013.
  abstract, arXiv:1206.6351, journal page
• A mixed method for Dirichlet problems with radial basis functions (with T. Tran)
  Comput. Math. Appl. 66 (10), 2045–2055, 2013.
  abstract, arXiv:1302.2079, journal page
• Robust DPG method for convection-dominated diffusion problems (with L. F. Demkowicz)
  SIAM J. Numer. Anal. 51 (5), 2514–2537, 2013.
  abstract, ICES Report 11-33, journal page
• Radial basis functions for the solution of hypersingular operators on open surfaces (with T. Tran)
  Comput. Math. Appl. 63 (11), 1504–1518, 2012.
  abstract, arXiv:1203.2912, journal page
• Natural hp-BEM for the electric field integral equation with singular solutions (with A. Bespalov)
  Numer. Methods Partial Differential Eq. 28 (5), 1466–1480, 2012.
  abstract, arXiv:1010.1459, journal page
• A Nitsche-based domain decomposition method for hypersingular integral equations (with F. Chouly)
  Numer. Math. 121 (4), 705–729, 2012.
  abstract, arXiv:1102.0202, journal page
• Hilbert scales and Sobolev spaces defined by associated Legendre functions (with V. Domínguez and F.–J. Sayas)
  J. Comput. Appl. Math. 235 (12), 3481–3501, 2011.
  abstract, arXiv:0909.4266, journal page
• A new H(div)-conforming p-interpolation operator in two dimensions (with A. Bespalov)
  ESAIM Math. Model. Num. Anal. 45 (2), 255–275, 2011.
  abstract, arXiv:0910.3891, journal page
• Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces (with A. Bespalov and R. Hiptmair)
  SIAM J. Numer. Anal. 48 (4), 1518–1529, 2010.
  abstract, arXiv:0907.5231, journal page, substitutes: abstract, arXiv:0810.3590
• Mortar boundary elements (with M. Healey)
  SIAM J. Numer. Anal. 48 (4), 1395–1418, 2010.
  abstract, arXiv:0901.4960, journal page
• Natural p-BEM for the electric field integral equation on screens (with A. Bespalov)
  IMA J. Numer. Anal. 30 (3), 595–628, 2010.
  abstract, preprint, journal page
• The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: a priori error analysis (with A. Bespalov)
  Appl. Numer. Math. 60 (7), 705–718, 2010.
  abstract, arXiv:0905.4946, journal page
• A direct coupling of local discontinuous Galerkin and boundary element methods (with G. N. Gatica and F.–J. Sayas)
  Math. Comp. 79 (271), 1369–1394, 2010.
  abstract, preprint, journal page
• The hp-version of the boundary element method with quasi-uniform meshes for weakly singular operators on surfaces (with A. Bespalov)
  IMA J. Numer. Anal. 30 (2), 377–400, 2010.
  abstract, preprint, journal page
• Optimal error estimation for H(curl)-conforming p-interpolation in two dimensions (with A. Bespalov)
  SIAM J. Numer. Anal. 47 (5), 3977–3989, 2009.
  abstract, arXiv:0903.4453, journal page
• The boundary element method with Lagrangian multipliers (with G. N. Gatica and M. Healey)
  Numer. Methods Partial Differential Eq. 25 (6), 1303–1319, 2009.
  abstract, preprint, journal page
• Crouzeix–Raviart boundary elements (with F.–J. Sayas)
  Numer. Math. 112 (3), 381–401, 2009.
  abstract, preprint, journal page
• A priori and a posteriori error analysis of an augmented mixed finite element method for incompressible fluid flows (with L. Figueroa and G. N. Gatica)
  Comput. Methods Appl. Mech. Engrg. 198 (2), 280–291, 2008.
  abstract, preprint, journal page
• The hp-version of the boundary element method with quasi-uniform meshes in three dimensions (with A. Bespalov)
  ESAIM Math. Model. Num. Anal. 42 (5), 821–849, 2008.
  abstract, preprint, journal page
• An extension theorem for polynomials on triangles (with F. Leydecker)
  Calcolo 45 (2), 69–85, 2008.
  abstract, preprint, journal page
• An iterative substructuring method for the hp-version of the BEM on quasi-uniform triangular meshes (with F. Leydecker and E. P. Stephan)
  Numer. Methods Partial Differential Eq. 23 (4), 879–903, 2007.
  abstract, preprint, journal page
• Numerical approximation of a time dependent, nonlinear, space-fractional order diffusion equation (with V. J. Ervin and J. P. Roop)
  SIAM J. Numer. Anal. 45 (2), 572–591, 2007.
  abstract, preprint, journal page
• The p-version of the boundary element method for weakly singular operators on piecewise plane open surfaces (with A. Bespalov)
  Numer. Math. 106 (1), 69–97, 2007.
  abstract, preprint, journal page
• On the finite element method for elliptic problems with degenerate and singular coefficients (with D. Arroyo and A. Bespalov)
  Math. Comp. 76 (258), 509–537, 2007.
  abstract, preprint, journal page
• A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity (with T. P. Barrios, G. N. Gatica and M. González)
  ESAIM Math. Model. Num. Anal. 40 (5), 843–869, 2006.
  abstract, preprint, journal page
• The optimal convergence of the h-p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains (with B. Q. Guo)
  Adv. Comput. Math., 24 (1–4), 353–374, 2006.
  abstract, preprint, journal page
• An adaptive boundary element method for the exterior Stokes problem in three dimensions (with V. J. Ervin)
  IMA J. Numer. Anal., 26 (2), 297–325, 2006.
  abstract, preprint, journal page
• The p-version of the boundary element method for a three-dimensional crack problem (with A. Bespalov)
  J. Integral Equations Appl. 17 (3), 243–258, 2005.
  abstract, preprint, journal page
• The p-version of the boundary element method for hypersingular operators on piecewise plane open surfaces (with A. Bespalov)
  Numer. Math. 100 (2), 185–209, 2005.
  abstract, preprint (ps.gz), journal page
• The optimal rate of convergence of the p-version of the boundary element method in two dimensions (with B. Q. Guo)
  Numer. Math. 98 (3), 499–538, 2004.
  abstract, preprint (ps.gz), journal page
• Approximation of time-dependent, viscoelastic fluid flow: Crank–Nicolson, finite element approximation (with V. J. Ervin)
  Numer. Methods Partial Differential Eq. 20 (2), 248–283, 2004.
  abstract, preprint (ps.gz), journal page
• An overlapping domain decomposition preconditioner for high order BEM with anisotropic elements (with Ernst P. Stephan)
  Adv. Comput. Math. 19 (1–3), 211–230, 2003.
  abstract, preprint (ps.gz), journal page
• On the numerical analysis of nonlinear twofold saddle point problems (with G. N. Gatica and S. Meddahi)
  IMA J. Numer. Anal. 23 (2), 301–330, 2003.
  abstract, preprint (ps.gz), journal page
• A preconditioned MINRES method for the coupling of mixed-FEM and BEM in some nonlinear problems (with G. N. Gatica)
  SIAM J. Sci. Comput. 24 (2), 572–596, 2002.
  abstract, preprint (ps.gz), journal page
• Conjugate gradient method for dual-dual mixed formulations (with G. N. Gatica)
  Math. Comp. 71 (240), 1455–1472, 2002.
  abstract, preprint (ps.gz), journal page
• An a posteriori error estimate for a linear-nonlinear transmission problem in plane elastostatics (with M. A. Barrientos and G. N. Gatica)
  Calcolo 39 (2), 61–86, 2002.
  abstract, preprint (ps.gz), journal page
• An hp-adaptive refinement strategy for hypersingular operators on surfaces
  Numer. Methods Partial Differential Eq. 18 (3), 396–419, 2002.
  abstract, preprint (ps.gz), journal page
• A posteriori error estimates for a mixed-FEM formulation of a nonlinear elliptic problem (with R. A. Araya, T. P. Barrios and G. N. Gatica)
  Comput. Methods Appl. Mech. Engrg. 191 (21–22), 2317–2336, 2002.
  abstract, preprint (ps.gz), journal page
• A p-adaptive algorithm for the BEM with the hypersingular operator on the plane screen (with M. E. Mellado and E. P. Stephan)
  Internat. J. Numer. Methods Engrg. 53 (1), 85–104, 2002.
  abstract, preprint (ps.gz), journal page
• hp-adaptive two-level methods for boundary integral equations on curves (with M. E. Mellado and E. P. Stephan)
  Computing 67 (4), 305–334, 2001.
  abstract, preprint (ps.gz), journal page
• An expanded mixed finite element approach via a dual-dual formulation and the minimum residual method (with G. N. Gatica)
  J. Comput. Appl. Math. 132 (2), 371–385, 2001.
  abstract, preprint (ps.gz), journal page
• Additive Schwarz method for the p-version of the boundary element method for the single layer potential operator on a plane screen
  Numer. Math. 88 (3), 485–511, 2001.
  abstract, preprint (ps.gz), journal page
• An additive Schwarz method for the h-p version of the boundary element method for hypersingular integral equations in R³ (with E. P. Stephan)
  IMA J. Numer. Anal. 21 (1), 265–283, 2001.
  abstract, preprint (ps.gz), journal page
• An implicit-explicit residual error estimator for the coupling of dual-mixed finite elements and boundary elements in elastostatics (with G. N. Gatica and E. P. Stephan)
  Math. Methods Appl. Sci. 24 (3), 179–191, 2001.
  abstract, preprint (ps.gz), journal page
• Minimum residual iteration for a dual-dual mixed formulation of exterior transmission problems (with G. N. Gatica)
  Numer. Linear Algebra Appl. 8 (3), 147–164, 2001.
  abstract, preprint (ps.gz), journal page
• A dual-dual formulation for the coupling of mixed-FEM and BEM in hyperelasticity (with G. N. Gatica)
  SIAM J. Numer. Anal., 38 (2), 380–400, 2000.
  abstract, preprint (ps.gz), journal page
• Schwarz method for systems of boundary integral equations
  Appl. Numer. Math., 33 (1–4), 447–453, 2000.
  abstract, journal page
• Additive Schwarz methods for indefinite hypersingular integral equations in R³ — the p-version
  Appl. Anal., 72 (3–4), 411–437, 1999.
  abstract, journal page
• Preconditioned minimum residual iteration for the h-p version of the coupled FEM/BEM with quasi-uniform meshes (with M. Maischak and E. P. Stephan)
  Numer. Linear Algebra Appl., 6 (6), 435–456, 1999.
  abstract, journal page
• Exponential convergence of the hp-version for the boundary element method on open surfaces (with M. Maischak and E. P. Stephan)
  Numer. Math., 83 (4), 641–666, 1999.
  abstract, journal page
• Iterative substructuring for hypersingular integral equations in R³ (with E. P. Stephan)
  SIAM J. Sci. Comput., 20 (2), 739–749, 1999.
  abstract, journal page
• Preconditioners for the p-version of the Galerkin method for a coupled finite element/boundary element system (with E. P. Stephan)
  Numer. Methods Partial Differential Eq., 14 (1), 47–61, 1998.
  abstract, journal page
• An iterative substructuring method for the p-version of the boundary element method for hypersingular integral equations in three dimensions
  Numer. Math., 79 (3), 371–396, 1998.
  abstract, journal page, erratum 87 (4), 793–794, 2001, journal page.
• Boundary integral operators in countably normed spaces (with E. P. Stephan)
  Math. Nachr., 191 (1), 123–151, 1998.
  abstract, journal page
• Multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method (with T. Tran and E. P. Stephan)
  Math. Comp., 67 (222), 501–518, 1998.
  abstract, journal page
• Efficient algorithms for the p-version of the boundary element method
  J. Integral Equations Appl., 8 (3), 337–361, 1996.
  abstract, journal page
• The hp-version of the boundary element method on polygons (with E. P. Stephan)
  J. Integral Equations Appl., 8 (2), 173–212, 1996.
  abstract, journal page
• The h-p version of the boundary element method for transmission problems with piecewise analytic data (with B. Q. Guo and E. P. Stephan)
  SIAM J. Numer. Anal., 33 (2), 789–808, 1996.
  abstract, journal page
• On the h-p version of the boundary element method for Symm's integral equation on polygons (with V. J. Ervin and E. P. Stephan)
  Comput. Methods Appl. Mech. Engrg., 110 (1–2), 25–38, 1993.
  abstract, journal page
• Mathematical model of a hot dry rock system (with T. Küpper and D. Windelberg)
  Geophys. J. Int., 105 (3), 659–664, 1991.
  abstract, journal page