%0 Journal Article %1 ISI:000364538800012 %A Betancourt, Fernando %A Rohde, Christian %C 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA %D 2016 %I ELSEVIER SCIENCE INC %J APPLIED MATHEMATICS AND COMPUTATION %K Finite-volume Friedrichs Relaxation formulation} schemes; systems; type {Involutionary %N 2 %P 420-439 %R 10.1016/j.amc.2015.03.050 %T Finite-volume schemes for Friedrichs systems with involutions %V 272 %X In applications solutions of systems of hyperbolic balance laws often have to satisfy additional side conditions. We consider initial value problems for the general class of Friedrichs systems where the solutions are constrained by differential conditions given in the form of involutions. These occur in particular in electrodynamics, electro- and magnetohydrodynamics as well as in elastodynamics. Neglecting the involution on the discrete level typically leads to instabilities. To overcome this problem in electrodynamical applications it has been suggested in Munz et al. (2000) to solve an extended system. Here we suggest an extended formulation to the general class of constrained Friedrichs systems. It is proven for explicit Finite-Volume schemes that the discrete solution of the extended system converges to the weak solution of the original system for vanishing discretization and extension parameter under appropriate scalings. Moreover we show that the involution is weakly satisfied in the limit. The proofs rely on a reformulation of the extension as a relaxation-type approximation and careful use of the convergence theory for finite-volume methods for systems of Friedrichs type. Numerical experiments illustrate Off analytical results. (C) 2015 Elsevier Inc. All rights reserved.

@article{ISI:000364538800012, abstract = {{In applications solutions of systems of hyperbolic balance laws often have to satisfy additional side conditions. We consider initial value problems for the general class of Friedrichs systems where the solutions are constrained by differential conditions given in the form of involutions. These occur in particular in electrodynamics, electro- and magnetohydrodynamics as well as in elastodynamics. Neglecting the involution on the discrete level typically leads to instabilities. To overcome this problem in electrodynamical applications it has been suggested in Munz et al. (2000) to solve an extended system. Here we suggest an extended formulation to the general class of constrained Friedrichs systems. It is proven for explicit Finite-Volume schemes that the discrete solution of the extended system converges to the weak solution of the original system for vanishing discretization and extension parameter under appropriate scalings. Moreover we show that the involution is weakly satisfied in the limit. The proofs rely on a reformulation of the extension as a relaxation-type approximation and careful use of the convergence theory for finite-volume methods for systems of Friedrichs type. Numerical experiments illustrate Off analytical results. (C) 2015 Elsevier Inc. All rights reserved.}}, added-at = {2017-05-18T11:32:12.000+0200}, address = {{360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA}}, affiliation = {{Rohde, C (Reprint Author), Univ Stuttgart, Inst Angew Anal \& Numer Simulat, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Betancourt, Fernando, Univ Concepcion, CI2MA, Concepcion, Chile. Betancourt, Fernando, Univ Concepcion, Dept Ingn Met, Concepcion, Chile. Rohde, Christian, Univ Stuttgart, Inst Angew Anal \& Numer Simulat, D-70569 Stuttgart, Germany.}}, author = {Betancourt, Fernando and Rohde, Christian}, author-email = {{fbentancourt@udec.cl crohde@mathematik.uni-stuttgart.de}}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21e820981add9bfdc75f57a508ec08daf/hermann}, doi = {{10.1016/j.amc.2015.03.050}}, eissn = {{1873-5649}}, funding-acknowledgement = {{Fondecyt project {[}11130397]; CRHIAM Fondap project {[}15130015]; BASAL project CMM; Universidad de Chile; Centro de Investigacion en Ingenicria Matematica {[}CI2 MA]; Univcrsidad de Concepcion; German Research Foundation (DFG) within the Cluster of Excellence in Simulation Technology at the University of Stuttgart {[}EXC 310/2]}}, funding-text = {{F.B. acknowledges support by Fondecyt project 11130397, CRHIAM Fondap project 15130015 and BASAL project CMM, Universidad de Chile and Centro de Investigacion en Ingenicria Matematica (CI2 MA), Univcrsidad de Concepcion. C.R. would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/2) at the University of Stuttgart.}}, interhash = {ed02ea7105dbf03775561e430c3835f4}, intrahash = {1e820981add9bfdc75f57a508ec08daf}, issn = {{0096-3003}}, journal = {{APPLIED MATHEMATICS AND COMPUTATION}}, keywords = {Finite-volume Friedrichs Relaxation formulation} schemes; systems; type {Involutionary}, keywords-plus = {{DISCONTINUOUS-GALERKIN METHODS; MAXWELL EQUATIONS; MHD EQUATIONS; CONVERGENCE}}, language = {{English}}, month = {{JAN 1}}, number = {{2}}, number-of-cited-references = {{31}}, pages = {{420-439}}, publisher = {{ELSEVIER SCIENCE INC}}, research-areas = {{Mathematics}}, times-cited = {{1}}, timestamp = {2017-05-18T09:32:12.000+0200}, title = {{Finite-volume schemes for Friedrichs systems with involutions}}, type = {{Article}}, volume = {{272}}, web-of-science-categories = {{Mathematics, Applied}}, year = {{2016}} }