0382310 20250807152153.120121116235959.9 000310992800004 10.1007/s00211-012-0474-8 15 s. cav_un_epca*02573460029-599X1224 (2012)709-723Springer measure-valued source diffusion equation cav_un_auth*0284719 Seidman T. US cav_un_auth*0284720 Gobbert M. US cav_un_auth*0284721 Trott D. US cav_un_auth*0101142 Kružík Martin Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2012/MTR/kruzik-finite element approximation for time-dependent diffusion with measure-valued source.pdf IAA100750802 GA AV ČR cav_un_auth*0241214 The convergence of finite element methods for elliptic and parabolic partial differential equations is well-established if source terms are sufficiently smooth. Noting that finite element computation is easily implemented even when the source terms are measure-valued—for instance, modeling point sources by Dirac delta distributions—we prove new convergence order results in two and three dimensions both for elliptic and for parabolic equations with measures as source terms. These analytical results are confirmed by numerical tests using COMSOL Multiphysics. 2013 BA 4 BA RVO:67985556 http://hdl.handle.net/11104/0212567 MATHEMATICSAPPLIED 1.668 0.316 >10.0 0.00886 1.409 4772 76 1.851 Q1 91.806 81.984 Q1* Q1 2012 000310992800004 WOS cav_un_epca*0257346 Numerische Mathematik 0029-599X 0945-3245 Roč. 122 č. 4 2012 709 723 Springer