Abstract
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution. Developing efficient and accurate solution strategies that account for errors on the space, time and parameter domains simultaneously is highly challenging. Indeed, it is well known that standard polynomialbased approximations on the parameter domain can incur errors that grow in time. In this work, we focus on advection–diffusion problems with parameterdependent wind fields. A novel adaptive solution strategy is proposed that allows users to combine stochastic collocation on the parameter domain with offtheshelf adaptive timestepping algorithms with local error control. This is a nonintrusive strategy that builds a polynomialbased surrogate that is adapted sequentially in time. The algorithm is driven by a socalled hierarchical estimator for the parametric error and balances this against an estimate for the global timestepping error which is derived from a scaling argument.
Original language  English 

Journal  Journal of Scientific Computing 
Publication status  Accepted/In press  10 May 2023 
Keywords
 parametric PDEs
 stochastic collocation
 adaptivity
 error estimation
Fingerprint
Dive into the research topics of 'Efficient Adaptive Stochastic Collocation Strategies for AdvectionDiffusion Problems with Uncertain Inputs'. Together they form a unique fingerprint.Impacts

IFISS: A software package for teaching computational mathematics
David Silvester (Participant), Howard Elman (Participant) & Alison Ramage (Participant)
Impact: Awareness and understanding, Technological