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

Publications

Preprints

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

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

[1] On interpolation spaces of piecewise polynomials on mixed meshes

M. Karkulik, J.M. Melenk, and A. Rieder
arXiv:2306.16907

In Journals

[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.