Long Title Your Name Joint work with X (from here), Y (from here) - - PowerPoint PPT Presentation

Long Title

Your Name Joint work with X (from here), Y (from here) and Z (from here)

Outline

1 Section 1 2 Section 2 3 Section 3 4 Section 4

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Section 1

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Frame Title

−ε∆u + b · ∇u = f in Ω ⊂ Rd u = 0

• n ∂Ω

Look at these equations...

Theorem

A Theorem −1 2∇ · b ≥ ρ ≥ 0.

Proof.

A Proof

• Your Name (Durham)

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Frame Title

There are some pictures below...

(a) ε = 0.1 (b) ε = 0.01 (c) ε = 0.001

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Another Frame

Some equations and pictures... −0.01∆u + (−1, 0)⊤ · ∇u = 1 in Ω ⊂ Rd u = 0

• n ∂Ω

0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(a) Standard plot

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

(b) Temperature map

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Section 2

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Frame Title

A definition...

Definition (Something to Define)

Some text... Bε(uh, v) := ε(∇uh, ∇v) + (b.∇uh, v) = (f, v) ∀v ∈ Vh.

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more?

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Section 3

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listing things... Γ the union of boundary faces (those in ∂Ω). For e ∈ Eo

h, T + is the downwind cell, T − the upwind cell as

determined by b · n on the face from each cell, n being the outward pointing normal. For e ∈ Eo

h the jump

{·} } are defined by

{ {ν} } = 1 2(ν+ + ν−), { {τ} } = 1 2(τ + + τ −). On the boundary these become

{ {ν} } = ν, { {τ} } = τ. A very useful identity

• T∈Th
• ∂T

ντ · n =

• e∈Eh

{τ} } +

• e∈Eo

h

{ {ν} }

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Section 4

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Future work on...

Idea 1. Idea 2. Idea 3. Extra info...

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References

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