What are source of error in flat elements traiangle finite element method? How can we improve it?

 

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Elements are flat triangular planes, nodes (x₁, y₁), (x2, y2), (X3, Y3) at corners 03 Again y(x, y) = y()(x, y) and U(y) = Uy(e)) (e) where Ne (e) In 2d, the interpolating function describing a triangle with nodes (x₁, y₁, 1), (x2, 12, 2), and (x3, y3, 3) is: N(e) N(e) $2 = Variation of (x, y) by adjusting the values $₁ Note: each node is usually shared between several adjacent elements = 3 y (e) (x, y) = N() (x, y)(e) i=1 2A(e) [(x2Y3X3Y2) + (V2 - Y3)x(x2x3)y] 1 2A(e) [(x31-X1Y3) + (V3 - Y₁)x - (x3 -x₁)y] 2A(e) [(x12x2Y1) + (y₁ - y₂)x - (x₁-x₂)y] Ae - area of the triangle Elements are flat triangular planes, nodes (x₁, y₁), (x2, y2), (X3, Y3) at corners 03 Again y(x, y) = y()(x, y) and U(y) = Uy(e)) (e) where Ne (e) In 2d, the interpolating function describing a triangle with nodes (x₁, y₁, 1), (x2, 12, 2), and (x3, y3, 3) is: N(e) N(e) $2 = Variation of (x, y) by adjusting the values $₁ Note: each node is usually shared between several adjacent elements = 3 y (e) (x, y) = N() (x, y)(e) i=1 2A(e) [(x2Y3X3Y2) + (V2 - Y3)x(x2x3)y] 1 2A(e) [(x31-X1Y3) + (V3 - Y₁)x - (x3 -x₁)y] 2A(e) [(x12x2Y1) + (y₁ - y₂)x - (x₁-x₂)y] Ae - area of the triangle

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Explanation The triangle inequality Lets ignore the issue of boundary approximation for a moment the... View the full answer