Michael Karkulik

Departamento de Matemática
Universidad Técnica Federico Santa María
Oficina 247
Avenida España 1680
Valparaíso, Chile

Email: michael.karkulik that special sign usm.cl

News : Research : Teaching : Links | Publications : Projects : Theses : Talks

Publications

in Journals, Preprints, Proceedings

Preprints

[2] Space-time FEM-BEM couplings for parabolic transmission problems: T. Führer, G. Gantner, and M. Karkulik
arXiv:2409.14449

[1] Well-posedness of first-order acoustic wave equations and space-time finite element approximation

T. Führer, R. González, and M. Karkulik
arXiv:2311.10536

In Journals

[36] On interpolation spaces of piecewise polynomials on mixed meshes: M. Karkulik, J.M. Melenk, and A. Rieder
accepted for publication in ESAIM Math. Model. Numer. Anal.,
arXiv:2306.16907
[35] Space-time finite element methods for parabolic distributed optimal control problems: T. Führer and M. Karkulik
accepted for publication in Comput. Methods Appl Math.
arXiv:2208.09879
[34] Least-squares finite elements for distributed optimal control problems: T. Führer and M. Karkulik
Numer. Math. 154, 2023, pp. 409--442
Springer, arXiv:2210.16377
[33] MINRES for second-order PDEs with singular data: T. Führer, N. Heuer, and M. Karkulik
SIAM J. Numer. Anal. 60(3), 2022, pp. 1111--1135
SIAM, arXiv:2111.00103
[32] Local convergence of the FEM for the integral fractional Laplacian: M. Faustmann, M. Karkulik, and J.M. Melenk
SIAM J. Numer. Anal., 60(3), 2022, pp. 1055--1082
SIAM, arXiv:2005.14109
[31] Analysis of backward Euler primal DPG methods: T. Führer, N. Heuer, and M. Karkulik
Comput. Methods Appl Math., 21(4), 2021, pp. 811--826
De Gruyter, arXiv:2103.12181
[30] Space-time least-squares finite elements for parabolic equations: T. Führer and M. Karkulik
Comput. Math. Appl., 92, 2021, pp. 27--36
Elsevier, arXiv:1911.01942
[29] A finite element method for elliptic Dirichlet boundary control problems: M. Karkulik
Comput. Methods Appl. Math., 20(4), 2020, pp. 827--843
arXiv:1811.09251
[28] Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D: M. Karkulik, J.M. Melenk, and A. Rieder
M2AN 54. 2020, pp. 145--180
arXiv:1811:11097
[27] H-matrix approximability of inverses of discretizations of the fractional Laplacian: M. Karkulik and J.M. Melenk
Adv. Comp. Math. 45, 2019, pp. 2893--2919
arXiv:1808.04274
[26] New a priori analysis of first-order system least-squares finite element methods for parabolic problems: T. Führer and M. Karkulik
Numer. Methods Partial Differential Equations 35, 2019
Wiley, arXiv:1805.04147
[25] Variational formulation of time-fractional parabolic equations: M. Karkulik
Comput. Math. Appl., 75(11) (2018), pp. 3929--3938
Elsevier, arXiv:1704:03257
[24] Combining the DPG method with finite elements: T. Führer, N. Heuer, M. Karkulik, R. Rodríguez
Comput. Methods Appl. Math., 18(4) (2018), pp. 639--652
De Gruyter, arXiv:1704.07471
[23] A robust DPG method for singularly perturbed reaction-diffusion problems: N. Heuer and M. Karkulik
SIAM J. Numer. Anal., 55(3) (2017), pp. 1218--1242
SIAM, arXiv.1509.07560
[22] DPG method with optimal test functions for a fractional advection diffusion equation: V.J. Ervin, T. Führer, N. Heuer, and M. Karkulik
J. Sci. Comput., 72(2) (2017), pp. 568--585
Springer, arXiv.1507.06691
[21] Discontinuous Petrov-Galerkin boundary elements: N. Heuer and M. Karkulik
Numer. Math., 135(4) (2017), pp. 1011--1043
Springer, arXiv.1408.5374
[20] Local inverse estimates for non-local boundary integral operators: M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, and D. Praetorius
Math. Comp., 86(308) (2017), pp. 2651--2686
AMS, ASC Report 12/2015, arXiv.1504.04394
[19] On the coupling of DPG and BEM: with T. Führer and N. Heuer
Math. Comp., 86(307) (2017), pp. 2261--2284
AMS, arXiv.1508.00630
[18] DPG method with optimal test functions for a transmission problem: with N. Heuer
Comput. Math. Appl., 70(5) (2015), pp. 1504--1518
Elsevier, arXiv.1411.4753
[17] Local high-order regularization and applications to hp-methods: with J.M. Melenk
Comput. Math. Appl., 70(7) (2015), pp. 1606--1639
Elsevier, ASC Report 38/2014, arXiv.1411.5209
[16] Adaptive Crouzeix-Raviart boundary element method: with N. Heuer
ESAIM Math. Model. Numer. Anal., 49(4) (2015), pp. 1193--1217
EDPS, PUC MAT2014-006, arXiv:1312.0484
[15] Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part II: Hyper-singular integral equation: with M. Feischl, T. Führer, J.M. Melenk, and D. Praetorius
Electron. Trans. Numer. Anal., 44 (2015), pp. 153--176
RICAM, ASC Report 30/2013
[14] Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems: with M. Feischl, T. Führer, and D. Praetorius
Numer. Math., 130(2) (2015), pp. 199--223
Springer, ASC Report 52/2012, arXiv:1212.2620
[13] Note on discontinuous trace approximation in the practical DPG method: with N. Heuer and F.-J. Sayas
Comput. Math. Appl., 68, (2014), pp. 1562--1568
Elsevier, PUC MAT2014-007, arXiv:1402.5169
[12] Adaptive boundary element methods: A posteriori error estimators, adaptivity, convergence, and implementation: M. Feischl, T. Führer, N. Heuer, M. Karkulik, D. Praetorius
Arch. Comput. Methods. Eng., 22(3) (2015), pp. 309--389
Springer, ASC Report 09/2014, PUC MAT2014-008, arXiv:1402.0744
[11] Energy norm based error estimators for adaptive BEM for hypersingular integral equations: M. Aurada, M. Feischl, T. Führer, M. Karkulik, D. Praetorius
Appl. Numer. Math., 95, (2015), pp. 15--35
Elsevier, ASC Report 22/2013
[10] ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve: M. Feischl, T. Führer, M. Karkulik, and D. Praetorius
Eng. Anal. Bound. Elem., 38 (2014), pp. 49--60.
Elsevier, ASC Report 16/2013, arXiv:1306.5120
[9] Quasi-optimal convergence rates for adaptive boundary element methods with data approximation, Part I: Weakly-singular integral equation: M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
Calcolo 51 (2014), pp. 485--508
Springer, ASC Report 24/2013
[8] HILBERT-A MATLAB Implementation of Adaptive 2D-BEM: M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, T. Führer, P. Goldenits, M. Karkulik, M. Mayr, and D. Praetorius
Numer. Algorithms 67(1) (2014), pp. 1--32
Springer, ASC Report 24/2011
[7] Efficiency and optimality of some weighted-residual error estimator for adaptive 2D boundary element methods: M. Aurada, M. Feischl, T. Führer, M. Karkulik, and D. Praetorius
Comput. Methods Appl. Math. 13(3) (2013), pp. 305--332
De Gruyter, ASC Report 15/2012
[6] On 2D newest vertex bisection: Optimality of mesh-closure and H^1-stability of L_2-projection: M. Karkulik, D. Pavlicek, and D. Praetorius
Constr. Approx. 38(2) (2013), pp. 213--234
Springer, ASC Report 10/2012, arXiv:1210.0367
[5] Convergence of adaptive 3D BEM for weakly singular integral equations based on isotropic mesh-refinement: M. Karkulik, G. Of, D. Praetorius
Numer. Methods Partial Differential Equations 29(6) (2013), pp. 2081--2106
Wiley, ASC Report 20/2012
[4] Quasi-optimal convergence rate for an adaptive boundary element method: M. Feischl, M. Karkulik, J.M. Melenk, and D. Praetorius
SIAM. J. Numer. Anal. 51(2) (2013), pp. 1327--1348
SIAM, Article, ASC Report 28/2011,
[3] Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity: M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, and D. Praetorius
Comp. Mech., 51 (2013), pp. 399--419.
Springer, ASC Report 8/2012, arXiv:1211.4225
[2] A posteriori error estimates for the Johnson-Nédélec FEM-BEM coupling: M. Aurada, M. Feischl, M. Karkulik, and D. Praetorius
Eng. Anal. Bound. Elem., 36 (2012), pp. 255--266.
Elsevier, ASC Report 18/2011
[1] Convergence of adaptive BEM for some mixed boundary value problem: M. Aurada, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, and D. Praetorius
Appl. Numer. Math., 62 (2012), pp. 226--245.
Elsevier, ASC Report 21/2010

Technical Reports

[3] L2-orthogonal projections onto lowest-order finite elements in Rd are H1-stable: M. Karkulik, C. M. Pfeiler, D. Praetorius
ASC Report 21/2013, arXiv:1307.0917
[2] Inverse estimates for elliptic boundary integral operators and their application to the adaptive coupling of FEM and BEM: M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, and D. Praetorius
ASC Report 07/2012
[1] HILBERT - a MATLAB implementation of adaptive BEM: M. Aurada, M. Ebner, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, and D. Praetorius
ASC Report 44/2009

Proceedings

[7] FEM-BEM couplings without stabilization: M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius
Proceedings of IABEM 2013, (2013)
ASC Report 47/2012
[6] Quasi-optimal adaptive BEM: M. Feischl, T. Führer, M. Karkulik, and D. Praetorius
Proceedings of IABEM 2013, (2013)
ASC Report 48/2012
[5] Novel inverse estimates for non-local operators: M. Feischl, T. Führer, M. Karkulik, J. Melenk, and D. Praetorius
Proceedings of IABEM 2013, (2013)
ASC Report 49/2012
[4] Residual a-posteriori error estimates in BEM: convergence of h-adaptive algorithms: M. Feischl, M. Karkulik, J. Melenk, and D. Praetorius
Proceedings of IABEM 2011, (2011)
ASC Report 21/2011
[3] Adaptive coupling of FEM and BEM: Simple error estimators and convergence: M. Aurada, M. Feischl, M. Karkulik, and D. Praetorius
Proceedings of IABEM 2011, (2011)
ASC Report 20/2011
[2] Adaptive coupling of FEM and BEM: Simple error estimators and convergence: M. Aurada, M. Feischl, M. Karkulik, and D. Praetorius
Proceedings in Applied Mathematics and Mechanics, PAMM, 11, (2011)
ASC Report 22/2011
[1] Adaptive coupling of FEM and BEM: Simple error estimators and convergence: M. Aurada, M. Feischl, M. Karkulik, and D. Praetorius
Proceedings of AfriCOMP 11, (2011)
ASC Report 35/2010

Projects

[3] Space-time finite element methods for parabolic problems: theory and applications: Principal Investigator, FONDECYT Regular project 1210579.; Funded by ANID Chile, April 2021 - March 2025.
[2] Fast space-time discretizations for fractional evolution equations: Principal Investigator, FONDECYT Regular project 1170672.; Funded by CONICYT Chile, April 2017 - March 2021.
[1] Efficient adaptive strategies for nonconforming boundary element methods: Principal Investigator, FONDECYT Postdoc project 3140614. Supervisor: Norbert Heuer.; Funded by CONICYT Chile, November 2013 - October 2015.

Theses

Zur Konvergenz und Quasioptimalität adaptiver Randelementmethoden: PhD thesis, Vienna University of Technology, October 2012
pdf
Quasi-Interpolation Operators for hp-Finite Element Methods: Masters's thesis, Vienna University of Technology, 2009

Talks

[-] Space-time finite elements for the wave equation: WONAPDE 2024, Concepción, Chile, 15.01.2024 - 19.01.2024.
[-] Space-time finite elements for the wave equation: XLIX Semana de la Matemática, Valparaíso, Chile, 10.10.2023 - 13.10.2023
[-] Towards space-time finite elements for the wave equation: ENUMATH 2023, Lisbon, Portugal, 04.09.2023 - 08.09.2023
[-] Space-time finite elements for the optimal control of parabolic equations: Minimum Residual and Least-Squares Finite Element Methods, Santiago, Chile, 5.10.2022 - 7.10.2022
[-] Space-time least squares finite elements for parabolic equations and applications: SIAM Conference on Computational Science and Engineering, virtual, 1.03.2021 - 5.03.2021
[-] Space-time least squares finite elements for parabolic equations and applications: French Latin-American Conference on New Trends in Applied Mathematics (Flacam 2019), Santiago, Chile, 5.11.2019 - 8.11.2019.
[-] Space-time least squares finite elements for parabolic equations and applications: Reliable Methods of Mathematical Modeling (RMMM 2019), Vienna, Austria, 9.09.2019 - 13.09.2019.
[-] Discrete interior regularity for the fractional Laplacian and approximation by H-matrices: WONAPDE 2019, Concepción, Chile, 21.01.2019 - 25.01.2019.
[-] Discrete interior regularity for the fractional Laplacian and approximation by H-matrices: Symposium of the International Association for Boundary Element Methods (IABEM). Paris, France, 26.06.2018 - 28.06.2018
[-] A robust DPG method for singularly perturbed reaction-diffusion problems: Minimum Residual and Least-Squares Finite Element Methods: Portland, USA, 02.10.2017 - 04.10.2017
[-] Variational formulation of time-fractional parabolic equations: Santiago Numerico III, Santiago, Chile, 28.06.2017 - 30.06.2017
[-] Discontinuous Petrov-Galerkin boundary elements: The first Chilean symposium on boundary element methods, Santiago, Chile, 14.12.2016.
[-] A robust DPG method for singularly perturbed reaction-diffusion problems: WONAPDE 2016, Concepción, Chile, 11.01.2016 - 15.01.2016.
[-] Convergence of adaptive FE/BE coupling methods: ENUMATH 2015 - European Conference on Numerical Mathematics and Advanced Applications, Ankara, Turkey, 14.09.2015 - 18.09.2015.
[-] Convergence of adaptive FE/BE coupling methods: COMCA 2015 - XXIV Congreso de Matemática Capricornio, Iquique, Chile, 05.08.2015 - 07.08.2015.
[-] Nonsymmetric coupling of boundary elements and ultraweak finite elements and DPG method with optimal test functions: 13th US National Congress on Computational Mechanics, San Diego, California, 26.07.2015 - 30.07.2015.
[-] DPG method with optimal test functions for a transmission problem: Caleta Numérica, Valparaíso, Chile, 05.12.2015.
[-] Nonsymmetric coupling of boundary elements and ultraweak finite elements and DPG method with optimal test functions: 1.st Pan-American Congress on Computational Mechanics, Buenos Aires, Argentina, 27.04.2015 - 29.04.2015.
[-] Local high-order regularization and applications to hp-methods: La Serena Numérica II, La Serena, Chile, 14.01.2015 - 16.01.2015.
[-] Nonconforming DPG method: CMAM 2014 - International Conference on Computational Methods in Applied Mathematics, St. Wolfgang, Austria, 28.09.2014 - 04.10.2014.
[-] Nonconforming DPG method: COMCA 2014 - XXIII Congreso de Matemática Capricornio, Universidad de Atacama, Copiapó, Chile, 06.08.2014 - 08.08.2014.
[-] DPG boundary elements with optimal test functions on surfaces: Valparaíso Numérico IV, Valparaíso, Chile, 11.12.2013 - 13.12.2013.
[-] On newest vertex bisection: Seminario de Análisis Numérico y Modelación Matemática, Universidad del Bío Bío, Concepción, 01.10.2013.
[-] Adaptive nonconforming boundary element methods: COMCA 2013 - XXII Congreso de Matemáticas, Universidad de La Serena, Chile, 31.07.2013 - 02.08.2013.
[-] Adaptive nonconforming boundary element methods: MAFELAP 2013, Brunel University, Uxbridge, England, 11.06.2013 - 14.06.2013.
[-] Quasi-optimal adaptive BEM: WONAPDE 2013, Concepción, Chile, 14.01.2013 - 18.01.2013.
[-] Novel inverse estimates for non-local operators: IABEM 2013 Conference, Santiago, Chile, 09.01.2013-11.01.2013.
[-] Quasi-optimal adaptive BEM: Valparaíso's Mathematics and its Applications Days (V-MAD III), Pontificia Universidad Católica de Valparaíso, Chile, 12.12.2012-14.12.2012.
[-] On the convergence and quasi-optimality of adaptive boundary element methods: Seminar of the Institute for Numerical Mathematics, Graz University of Technology, 07.11.2012.
[-] Novel inverse estimates for non-local operators: 10th Workshop on Fast Boundary Element Methods in Industrial Applications, Hirschegg/Kleinwalsertal, 27.09.2012-30.09.2012.
[-] Quasi-optimal convergence rate for an adaptive boundary element method: Computational Methods in Applied Mathematics CMAM-5, Berlin, 30.07.2012-03.08.2012.
[-] A survey on adaptive boundary element methods: Fast BEM and BETI, Ostrava (Tschechien), 18.06.2012-19.06.2012.
[-] On 2D Newest Vertex Bisection: Optimality of Mesh-Closure and H1 Stability of L2-Projection: 8th Austrian Numerical Analysis Day, Wien, 10.05.2012-11.05.2012
[-] Quasi-optimal convergence rate for an adaptive boundary element method: BEM on the Saar 2012, Universität des Saarlandes, 12.05.2012-16.05.2012.
[-] Residual a-posteriori error estimates in BEM: convergence of h-adaptive algorithms: IABEM 2011 Conference, Brescia, 05.09.2011-08.09.2011.
[-] hp-Quasi-Interpolation: Poster: Junior Scientist Conference, The City College of New York, 13.04.2011-15.04.2011.
[-] Application of Interpolation theory to adaptive 3D-BEM: 8th Söllerhaus Workshop on Fast Boundary Element Methods in Industrial Applications, Hirschegg/Kleinwalsertal, 30.09.2010-03.10.2010.
[-] HILBERT - A Matlab Library for Adaptive 2D BEM: 6th Austrian Numerical Analysis Day, Salzburg, 06.05.2010-07.05.2010
[-] Convergence of Data-Perturbed Adaptive Boundary Element Methods: WONAPDE 2010, Concepción (Chile), 11.01.2010-15.01.2010.