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Applications of adaptivity in verified numerics

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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

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Title

Applications of adaptivity in verified numerics

Alternative Title

Applications of moving mesh methods in rigorous computing

Title of Series

Adaptive Numerical Methods for Partial Differential Equations with Applications (18w5148)

Number of Parts

21

Author

License

CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.

Identifiers

10.5446/59112 (DOI)

Publisher

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

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Subject Area

Computer Science Mathematics Physics

Genre

Workshop/Interactive Format Lecture

Abstract

This talk will introduce the field of rigorous computing and explain some of the problems it solves and tools it requires in a classical fixed grid context. We will then consider continuation problems where moving meshes are particularly useful. r-adaptive methods provide numerical efficiency and also simplify some of the topological technicalities in this approach.

Series

Adaptive Numerical Methods for Partial Differential Equations with Applications (18w5148)19 / 21

1

36:08

MMPDE moving mesh smoothing

2

28:04

Moving mesh finite difference method for non-monotone two-phase flows in porous media

3

30:24

New Analysis of Fully Discrete FEMs for Nonlinear Parabolic PDEs

4

39:40

Note on Spatial adaptations for the numerical solution of singular reaction-diffusion equations

5

39:28

Extending BACOLI to solve Multi-Scale Models

6

33:26

B-spline adaptive collocation/Runge-Kutta software with interpolation-based spatial error estimation for the error-controlled numerical solution of PDEs

7

33:57

Parallel PDE based mesh generators

8

25:31

Combining h- and r-adaptivity for finite-element models with jumping coefficients

9

1:01:04

Adaptive moving meshes in large eddy simulation for turbulent flows

10

1:00:31

A moving mesh discontinuous Galerkin method for hyperbolic conservation laws

11

40:58

A posteriori error estimation on anisotropic meshes

12

37:50

Monge-Ampére methods for fourth order PDEs and applications to elastic interface problems

13

38:50

Bistable traveling waves under discretization: moving meshes

14

29:51

Adaptive and non-adaptive spline collocation methods for a discontinuous diffusion PDE with application to brain cancer growth

15

54:03

Finite element method on polygonal meshes

16

38:07

A parallel variational mesh quality improvement method for distributed memory machines

17

41:54

Continuous and discontinuous approaches to moving mesh finite elements

18

1:05:52

Mesh adaptivity on the sphere using optimal transport, and a moving mesh scheme for the nonlinear shallow water equations

19

45:36

Applications of adaptivity in verified numerics

20

27:28

A surface moving mesh method based on equidistribution and alignment

21

1:01:56

An adaptive moving mesh method for geometric evolution laws and bulk-surface PDEs

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