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SUMMARY:Difference schemes stabilized by discrete mollification for degene
 rate parabolic equations in two space dimensions
DTSTART:20110518T161500
DTSTAMP:20260407T084900Z
UID:0d7beab4c948f6ba7eb14c68c7c0a87f0280540126ff0106ea8e6e26
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Raimund Bürger\nThe discrete mollification method is a 
 convolution-based filtering procedure for the regularization of ill-posed 
 problems. This method is applied here to stabilize explicit schemes\, whic
 h were first analyzed by Karlsen and Risebro (M2AN  35 (2001)\, 239-269)\,
  for the solution of initial value problems of strongly degenerate parabol
 ic PDEs in two space dimensions. Two new schemes are proposed\, which are 
 based on direction-wise and two-dimensional discrete mollification of the 
 second partial derivatives forming the Laplacian of the diffusion function
 \, respectively. The mollified schemes permit to use substantially larger 
 time steps than the original (basic) scheme.   \nIt is proven that both sc
 hemes converge to the unique entropy solution of the initial value problem
 . Numerical examples demonstrate that the mollified schemes are competitiv
 e in efficiency\, and in many cases significantly more efficient\, than th
 e basic scheme.\nThis presentation is based on joint work with Carlos D. A
 costa (Universidad Nacional de Colombia\, Sede Manizales).
LOCATION:MA A110
STATUS:CONFIRMED
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