# Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractability

@inproceedings{Sli2006FiniteEA, title={Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractability}, author={Endre S{\"u}li}, year={2006} }

Partial differential equations with nonnegative characteristic form arise in numerous
mathematical models of physical phenomena: stochastic analysis, in particular, is a fertile
source of equations of this kind. We survey recent developments concerning the finite element
approximation of these equations, focusing on three relevant aspects: (a) stability and stabilisation;
(b) hp-adaptive algorithms driven by residual-based a posteriori error bounds, capable of
automatic variation of the…

## One Citation

Sparse finite element approximation of high-dimensional transport-dominated diffusion problems

- Mathematics
- 2008

We develop the analysis of stabilized sparse tensor-product finite element methods for high-dimensional, non-self-adjoint and possibly degenerate second-order partial differential equations of the…

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