Let T be a rectangle with vertices x0, x1, x2, and x3 (in this order, counter-clockwise)....
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Let T be a rectangle with vertices x0, x1, x2, and x3 (in this order, counter-clockwise). Further, define a space of bivariate polynomials as follows P ={a + B₁ +y§2 + 8§1&2 | (α, ß, y, 8) € R¹}. (1) Set (Vie {0, 1,2,3}) ; (v) = v(x₁). Show that (T, P, {Yo, V1, V2, V3}) is a finite element. (ii) Define v ( xi + Xi+1). 2 with the convention that x4 = xo. Show that (T, P, {P0, P1, P2, P3}) is not a finite element. (Vie {0, 1, 2, 3}) Ø; (v) = V Let T be a rectangle with vertices x0, x1, x2, and x3 (in this order, counter-clockwise). Further, define a space of bivariate polynomials as follows P ={a + B₁ +y§2 + 8§1&2 | (α, ß, y, 8) € R¹}. (1) Set (Vie {0, 1,2,3}) ; (v) = v(x₁). Show that (T, P, {Yo, V1, V2, V3}) is a finite element. (ii) Define v ( xi + Xi+1). 2 with the convention that x4 = xo. Show that (T, P, {P0, P1, P2, P3}) is not a finite element. (Vie {0, 1, 2, 3}) Ø; (v) = V
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0471669593
9th edition
Authors: Howard Anton, Chris Rorres
Posted Date:
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