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New Discretization Methods for the Numerical Approximation of PDEs

dc.date.accessioned2019-10-24T15:01:12Z
dc.date.available2019-10-24T15:01:12Z
dc.date.issued2015
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3449
dc.description.abstractThe construction and mathematical analysis of numerical methods for PDEs is a fundamental area of modern applied mathematics. Among the various techniques that have been proposed in the past, some – in particular, finite element methods, – have been exceptionally successful in a range of applications. There are however a number of important challenges that remain, including the optimal adaptive finite element approximation of solutions to transport-dominated diffusion problems, the efficient numerical approximation of parametrized families of PDEs, and the efficient numerical approximation of high-dimensional partial differential equations (that arise from stochastic analysis and statistical physics, for example, in the form of a backward Kolmogorov equation, which, unlike its formal adjoint, the forward Kolmogorov equation, is not in divergence form, and therefore not directly amenable to finite element approximation, even when the spatial dimension is low). In recent years several original and conceptionally new ideas have emerged in order to tackle these open problems. The goal of this workshop was to discuss and compare a number of novel approaches, to study their potential and applicability, and to formulate the strategic goals and directions of research in this field for the next five years.
dc.titleNew Discretization Methods for the Numerical Approximation of PDEs
dc.identifier.doi10.14760/OWR-2015-2
local.series.idOWR-2015-2
local.subject.msc42
local.subject.msc65
local.subject.msc35
local.subject.msc41
local.sortindex889
local.date-range11 Jan - 17 Jan 2015
local.workshopcode1503
local.workshoptitleNew Discretization Methods for the Numerical Approximation of PDEs
local.organizersStephan Dahlke, Marburg; Gitta Kutyniok, Berlin; Rob Stevenson, Amsterdam; Endre Süli, Oxford
local.report-nameWorkshop Report 2015,2
local.opc-photo-id1503
local.publishers-doi10.4171/OWR/2015/2
local.ems-referenceDahlke Stephan, Kutyniok Gitta, Stevenson Rob, Süli Endre: New Discretization Methods for the Numerical Approximation of PDEs. Oberwolfach Rep. 12 (2015), 87-185. doi: 10.4171/OWR/2015/2


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