TY - JOUR AU - Pereira, M AU - Kulcsar, Balazs AU - Lipták, György AU - Kovács, Mihály AU - Szederkényi, Gábor TI - The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling JF - TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES J2 - TRANSPORT RES C-EMER VL - 158 PY - 2024 PG - 13 SN - 0968-090X DO - 10.1016/j.trc.2023.104435 UR - https://m2.mtmt.hu/api/publication/34415352 ID - 34415352 N1 - Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden Institute for Computer Science and Control (SZTAKI), Budapest, Hungary Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary Center for Geosciences and Geoengineering, Mines Paris - PSL University, Fontainebleau, France Export Date: 18 December 2023 Correspondence Address: Pereira, M.; Department of Electrical Engineering, Sweden; email: mike.pereira@minesparis.psl.eu LA - English DB - MTMT ER - TY - JOUR AU - Bolin, David AU - Kovács, Mihály AU - Kumar, Vivek AU - Simas, Alexandre B. TI - REGULARITY AND NUMERICAL APPROXIMATION OF FRACTIONAL ELLIPTIC DIFFERENTIAL EQUATIONS ON COMPACT METRIC GRAPHS JF - MATHEMATICS OF COMPUTATION J2 - MATH COMPUT PY - 2023 PG - 34 SN - 0025-5718 DO - 10.1090/mcom/3929 UR - https://m2.mtmt.hu/api/publication/34646798 ID - 34646798 N1 - Funding Agency and Grant Number: Marsden Fund of the Royal Society of New Zealand [18-UOO-143]; Swedish Research Council (VR) [2017-04274]; National Research, Development, and Innovation Fund of Hungary [TKP2021-NVA-02, K-131545]; NBHM post-doctoral fellowship from the Department of Atomic Energy (DAE), Government of India [0204/6/2022/RD-II/5635] Funding text: The second author was supported by the Marsden Fund of the Royal Society of New Zealand (grant no. 18-UOO-143), the Swedish Research Council (VR) (grant no. 2017-04274) and the National Research, Development, and Innovation Fund of Hungary (grant no. TKP2021-NVA-02 and K-131545). The third author was supported in part by a NBHM post-doctoral fellowship from the Department of Atomic Energy (DAE), Government of India (file no. 0204/6/2022/R&D-II/5635). LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Vághy, Mihály András TI - Nonlinear semigroups for nonlocal conservation laws JF - Partial Differential Equations and Applications J2 - Partial Differ. Equ. Appl. VL - 4 PY - 2023 IS - 4 PG - 26 SN - 2662-2963 DO - 10.1007/s42985-023-00249-9 UR - https://m2.mtmt.hu/api/publication/34069695 ID - 34069695 N1 - Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, SE-41296, Sweden Department of Analysis and Operations Research, Institute of Mathematics, Budapest University of Technology and Economics, Müegyetem rkp. 3, Budapest, 1111, Hungary Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, Budapest, 1444, Hungary Export Date: 20 July 2023 Correspondence Address: Kovács, M.; Department of Analysis and Operations Research, Müegyetem rkp. 3, Hungary; email: mkovacs@math.bme.hu LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Sikolya, Eszter TI - On the parabolic Cauchy problem for quantum graphs with vertex noise JF - ELECTRONIC JOURNAL OF PROBABILITY J2 - ELECTRON J PROBAB VL - 28 PY - 2023 SN - 1083-6489 DO - 10.1214/23-EJP962 UR - https://m2.mtmt.hu/api/publication/34048342 ID - 34048342 N1 - Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden Department of Differential Equations, Budapest University of Technology and Economics, Budapest, Hungary Hungary and Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary Export Date: 6 July 2023 AB - We investigate the parabolic Cauchy problem associated with quantum graphs includ-ing Lipschitz or polynomial type nonlinearities and additive Gaussian noise perturbed vertex conditions. The vertex conditions are the standard continuity and Kirchhoff assumptions in each vertex. In the case when only Kirchhoff conditions are perturbed, we can prove existence and uniqueness of a mild solution with continuous paths in the standard state space 9-L of square integrable functions on the edges. We also show that the solution is Markov and Feller. Furthermore, assuming that the vertex values of the normalized eigenfunctions of the self-adjoint operator governing the problem are uniformly bounded, we show that the mild solution has continuous paths in the fractional domain space associated with the Hamiltonian operator, 9-L & alpha; for & alpha; < 14. This is the case when the Hamiltonian operator is the standard Laplacian perturbed by a potential. We also show that if noise is present in both type of vertex conditions, then the problem admits a mild solution with continuous paths in the fractional domain space 9-L & alpha; with & alpha; < -14 only. These regularity results are the quantum graph ana-logues obtained by da Prato and Zabczyk [9] in case of a single interval and classical boundary Dirichlet or Neumann noise. LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Lang, Annika AU - Petersson, Andreas TI - Approximation of SPDE covariance operators by finite elements: a semigroup approach JF - IMA JOURNAL OF NUMERICAL ANALYSIS J2 - IMA J NUMER ANAL VL - 43 PY - 2023 IS - 3 SP - 1324 EP - 1357 PG - 34 SN - 0272-4979 DO - 10.1093/imanum/drac020 UR - https://m2.mtmt.hu/api/publication/32896300 ID - 32896300 N1 - Funding Agency and Grant Number: Marsden Fund of the Royal Society of New Zealand [18-UOO-143]; Swedish Research Council(VR) [2017-04274, 2020-04170, 621-2014-3995]; National Research, Development, and Innovation Fund of Hungary [131545, TKP2021-NVA-02]; Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation; Chalmers AI Research Centre (CHAIR); Research Council of Norway [274410]; Knut and Alice Wallenberg foundation Funding text: Marsden Fund of the Royal Society of New Zealand (18-UOO-143toM.K.); Swedish Research Council(VR)(2017-04274 to M.K., 2020-04170 to A.L., 621-2014-3995 to A.P.); National Research, Development, and Innovation Fund of Hungary (131545 and TKP2021-NVA-02 to M.K.); Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation(toA.L.); Chalmers AI Research Centre (CHAIR)(toA.L.); Research Council of Norway (274410 to A.P.); Knut and Alice Wallenberg foundation(toA.P.). AB - The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error decomposition is proven. This formula is applied to approximations of the covariance operator of a stochastic advection-diffusion equation and a stochastic wave equation, both on bounded domains. The approximations are based on finite element discretizations in space and rational approximations of the exponential function in time. Convergence rates are derived in the trace class and Hilbert-Schmidt norms with numerical simulations illustrating the results. LA - English DB - MTMT ER - TY - JOUR AU - Fahim, K. AU - Hausenblas, E. AU - Kovács, Mihály TI - Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise JF - STOCHASTICS PARTIAL DIFFERENTIAL EQUATIONS: ANALYSIS AND COMPUTATIONS J2 - STOCHASTICS PARTIAL DIFFERENTIAL EQUATIONS VL - 11 PY - 2023 IS - 3 SP - 1044 EP - 1088 PG - 45 SN - 2194-0401 DO - 10.1007/s40072-022-00250-0 UR - https://m2.mtmt.hu/api/publication/32813160 ID - 32813160 N1 - Department of Mathematics, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Surabaya, 60111, Indonesia Department of Mathematics, Montanuniversity Leoben, Leoben, 8700, Austria Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary Department of Differential Equations, Faculty of Natural Sciences, Budapest University of Technology and Economics, Müegyetem rkp. 3., Budapest, 1111, Hungary Chalmers University of Technology, Gothenburg, Sweden Export Date: 10 May 2022 Correspondence Address: Kovács, M.; Chalmers University of TechnologySweden; email: kovacs.mihaly@itk.ppke.hu LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Lang, Annika AU - Petersson, Andreas TI - Hilbert-Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations JF - STOCHASTIC ANALYSIS AND APPLICATIONS J2 - STOCH ANAL APPL VL - 41 PY - 2023 IS - 3 SP - 564 EP - 590 PG - 27 SN - 0736-2994 DO - 10.1080/07362994.2022.2053541 UR - https://m2.mtmt.hu/api/publication/32811394 ID - 32811394 N1 - Funding Agency and Grant Number: Royal Society of New ZealandRoyal Society of New Zealand [18-UOO-143]; Swedish Research Council (VR)Swedish Research Council [2017-04274, 2020-04170, 621-2014-3995]; NKFIHNational Research, Development & Innovation Office (NRDIO) - Hungary [131545, TKP2021-NVA-02]; Wallenberg AI, Autonomous Systems and Software Program (WASP) - Knut and Alice Wallenberg Foundation; Chalmers AI Research Center (CHAIR); Research Council of Norway (RCN)Research Council of Norway [274410]; Knut and Alice Wallenberg foundationKnut & Alice Wallenberg Foundation Funding text: M. Kovacs acknowledges the support of the Marsden Fund of the Royal Society of New Zealand through grant. no. 18-UOO-143, the Swedish Research Council (VR) through project no. 2017-04274 and the NKFIH through grant numbers 131545 and TKP2021-NVA-02. The work of A. Lang was partially supported by the Swedish Research Council (VR) (project no. 2020-04170), by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation, and by the Chalmers AI Research Center (CHAIR). The work of A. Petersson was supported in part by the Research Council of Norway (RCN) through project no. 274410, the Swedish Research Council (VR) through reg. no. 621-2014-3995 and the Knut and Alice Wallenberg foundation. AB - Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates are of the form of Hilbert-Schmidt norms of the integral operator and its square root, composed with fractional powers of an elliptic operator equipped with homogeneous boundary conditions of either Dirichlet or Neumann type. These types of estimates, which couple the regularity of the driving noise with the properties of the differential operator, have important implications for stochastic partial differential equations on bounded domains as well as their numerical approximations. The main tools used to derive the estimates are properties of reproducing kernel Hilbert spaces of functions on bounded domains along with Hilbert-Schmidt embeddings of Sobolev spaces. Both non-homogeneous and homogeneous kernels are considered. In the latter case, results in a general Schatten class norm are also provided. Important examples of homogeneous kernels covered by the results of the paper include the class of Matern kernels. LA - English DB - MTMT ER - TY - JOUR AU - Jansson, Erik AU - Kovács, Mihály AU - Lang, Annika TI - SURFACE FINITE ELEMENT APPROXIMATION OF SPHERICAL WHITTLE--MAT\\'ERN GAUSSIAN RANDOM FIELDS JF - SIAM JOURNAL ON SCIENTIFIC COMPUTING J2 - SIAM J SCI COMPUT VL - 44 PY - 2022 IS - 2 SP - A825 EP - A842 SN - 1064-8275 DO - 10.1137/21M1400717 UR - https://m2.mtmt.hu/api/publication/33193060 ID - 33193060 AB - Spherical Whittle--Mate'\rn Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the nonfractional part of the operator is solved by a recursive scheme, a quadrature of the Dunford-Taylor integral representation is employed for the fractional part. Strong error analysis is performed, and the computational complexity is bounded in terms of the accuracy. Numerical experiments for different choices of parameters confirm the theoretical findings. LA - English DB - MTMT ER - TY - JOUR AU - Vághy, Mihály András AU - Kovács, Mihály AU - Szederkényi, Gábor TI - Kinetic discretization of one-dimensional nonlocal flow models JF - IFAC PAPERSONLINE J2 - IFACOL VL - 55 PY - 2022 IS - 20 SP - 67 EP - 72 PG - 6 SN - 2405-8971 DO - 10.1016/j.ifacol.2022.09.073 UR - https://m2.mtmt.hu/api/publication/33124279 ID - 33124279 LA - English DB - MTMT ER - TY - JOUR AU - Baeumer, Boris AU - Kovács, Mihály AU - Parry, Matthew TI - A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains JF - FRACTIONAL CALCULUS AND APPLIED ANALYSIS J2 - FRACT CALC APPL ANAL VL - 25 PY - 2022 IS - 1 SP - 299 EP - 319 PG - 21 SN - 1311-0454 DO - 10.1007/s13540-021-00013-z UR - https://m2.mtmt.hu/api/publication/32916676 ID - 32916676 N1 - Funding Agency and Grant Number: Marsden grant Funding text: This work is partially funded by a Marsden grant administered by the Royal Society of New Zealand. The authors would like to thank Dr Lorenzo Toniazzi and Professor Christian Lubich for many valuable discussions. AB - We develop a finite difference approximation of order alpha for the alpha-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Grunwald scheme. In particular, approximate solutions to fractional diffusion equations preserve positivity. Furthermore, for the approximation of the solution to the skewed fractional heat equation on a bounded domain the new approximation scheme keeps its order alpha whereas the order of the Grunwald scheme reduces to order alpha - 1, contradicting the convergence rate results by Meerschaert and Tadjeran. LA - English DB - MTMT ER -