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cao's numerical method for solving SPDE

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cao's numerical method for solving SPDE
FINITE ELEMENT APPROXIMATIONS FOR
SPDES WITH WHITE NOISE FORCING TERMS
Yanzhao Cao
Department of Mathematics & Statistics
Auburn University

November 20, 2009

Yanzhao Cao

Numerical SPDES

November 20, 2009

1 / 35

Outline
1

Introduction
Brownian sheet and elliptic SPDE

Yanzhao Cao

Numerical SPDES

November 20, 2009

2 / 35

Outline
1

Introduction
Brownian sheet and elliptic SPDE

2

SPDE with discretized white noise
˙
Discretization of white noise Wh
Error estimate

Yanzhao Cao

Numerical SPDES

November 20, 2009

2 / 35

Outline
1

Introduction
Brownian sheet and elliptic SPDE

2

SPDE with discretized white noise
˙
Discretization of white noise Wh
Error estimate

3

Finite element approximation of elliptic SPDE
Finite element solution Uh

Yanzhao Cao

Numerical SPDES

November 20, 2009

2 / 35

Outline
1

Introduction
Brownian sheet and elliptic SPDE

2

SPDE with discretized white noise
˙
Discretization of white noise Wh
Error estimate

3

Finite element approximation of elliptic SPDE
Finite element solution Uh

4

Finite element approximations of stochastic Stokes equations
Stochastic Stokes Equations

Yanzhao Cao

Numerical SPDES

November 20, 2009

2 / 35

Outline
1

Introduction
Brownian sheet and elliptic SPDE

2

SPDE with discretized white noise
˙
Discretization of white noise Wh
Error estimate

3

Finite element approximation of elliptic SPDE
Finite element solution Uh

4

Finite element approximations of stochastic Stokes equations
Stochastic Stokes Equations

5

Numerical experiments
Numerical experiments
Yanzhao Cao

Numerical SPDES

November 20, 2009

2 / 35

1

Introduction
Brownian sheet and elliptic SPDE

2

SPDE with discretized white noise
˙
Discretization of white noise Wh
Error estimate

3

Finite element approximation of elliptic SPDE
Finite element solution Uh

4
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