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 and Reports, Proceedings

In Journals

[24] Combining the DPG method with finite elements
T. Führer, N. Heuer, M. Karkulik, R. Rodríguez
Comput. Methods Appl. Math.
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
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
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
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

Preprints and Technical Reports

[4] Variational formulation of time-fractional parabolic equations
M. Karkulik
arXiv:1704:03257
[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

[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

[-] 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.