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Basis functions v k (blue) and a linear combination of them, which is piecewise linear (red).

A continuous functio n , with zero values at the endpoints (blue), and a piecewise linear approximation (red). N 1 ( x ). N 1 ( x ). Basis functions v k (blue) and a linear combination of them, which is piecewise linear (red). A piecewise linear function in two dimensions. p 1 ( x , y ).

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Basis functions v k (blue) and a linear combination of them, which is piecewise linear (red).

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  1. A continuous function, with zero values at the endpoints (blue), and a piecewise linear approximation (red).

  2. N1(x) N1(x) Basis functions vk (blue) and a linear combination of them, which is piecewise linear (red).

  3. A piecewise linear function in two dimensions.

  4. p1(x,y) p2(x,y) p3(x,y)

  5. 3 2 3 W2 W1 1 1 1 4 3 2 2 =

  6. + = = = -

  7. Solving the two-dimensional problem uxx + uyy = − 4 in the disk centered at the origin and radius 1, with zero boundary conditions.The triangulation.

  8. The computed solution, u(x,y) = 1 − x2 − y2.

  9. The sparse matrixA of the discretized linear system.

  10. 2D FEM solution for a magnetostatic configuration (lines denote the direction of calculated flux density and colour - its magnitude) 2D mesh for the image (mesh is denser around the object of interest)

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