T3 finite element is defined over AABC (in physical coordiinates). The vertices of this triangle have the followi...
T3 finite element is defined over AABC (in physical coordinates). The vertices of this triangle hav the following coordinates: A(-2,-1), B(3,2), and C(0,6). Problem 2 a) Using 1 point and 3 point integration rules, compute f(x, y)ds AABC 2x2-3xy + y2. where f(x,y) Which rule gives more accurate result? c) What is the integration error, if 3 point rule is used? (Hint: for what polynomial degree 3 point rule gives the exact result?) b)
T3 finite element is defined over...
Problem 3. (15 points) T3 finite element is defined over AABC (in physical coordinates). The vertices of this triangle have the following coordinates: A(-3, -5), B(2,-1), and C(-6, 4) f(x, y)dS ДАВС where f(x, y) 3 2х?-5у? + 3ху+x — у. Bonus problem (5 extra points) a) Solve Problem 3 using 3 point integration rule. b) Which rule (1 point or 3 point) gives more accurate result? c) What is the integration error, if 3 point rule is used?
Problem...
O CWOIK 2. Submission deadline: 11:59pm on Friday June 7, 2019 Penalty for late submission: 20% per day T3 finite element is defined over AABC (in physical coordinates). The vertices of this triangle have the following coordinates: A(-2, -1), B(3,2), and C(0, 6). Problem 1 Calculate the partial derivatives of T3 basis functions with respect to the physical coordinates x and y. Problem 2. a) Using 1 point and 3 point integration rules, compute f(x, y)ds AABC where f(x,y) =2x2-3xy...
Function f(x, y) 2x2-3x +5y - y2 is going to be represented by T3 basis functions over AABC. Calculate the values of the degrees of freedom Ci in the linear combination that represents f(x,y): f(x, y)- CiN(x, y) T3 finite element is defined over ΔABC (in physical coordinates). The vertices of this triangle have the following coordinates: A(-2,-1), B(3,2), and C(0, 6) Problem 1
Function f(x, y) 2x2-3x +5y - y2 is going to be represented by T3 basis functions...
Exercise 2: Finite element method We are interested in computing numerically the solution to a 2D Laplace equation u 0, The triangulated domain is given in the file mesh.mat on Blackboard. which contains the V × 2 nnatrix vertices storing the two coordinates of the vertices and a F × 3 matrix triangles in which each ro w J contains the indices in {1,····V) of the three vertices of the j-th triangle. a) Using for example MATLAB's triplot or trimesh...
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Dry - xdA over the triangle with vertices ( -1,0), (0,0) and (0,1) changing the variables by u = y - x and v = y + x. (DONOTEVALUATE INTEGRAL) 1 w 5. (15 points) Write the integral representing the area of the region al < x2 + y2 < band below the line y = x in polar coordinates.(DONOT EVALUATE INTEGRAL) ,y,z) as an iterated integral in cartesian coor- dinates. E is the region inside...
Use your rules for translations and reflections to create a picture. You may do this on paper or using a computer program, such as Geogebra. Follow each step, in o 1. Graph a hexagon with vertices at (-4, 0), (-2, 0)·(-1,-1), (-2,-2), (-4,-2), and (-5,-1). 2. In the center of the hexagon, label it A. 3. Reflect hexagon A across the y-axis 4. Label the reflected hexagon A 5. Go bak to hexagon A, and translate it using the rule...
solve and show all work please
15.4 Integration in polar cylindrical spherical coordinates: Problem7 Previous Problem Problem List Next Problern (1 point Use sphenical coordinates to calculate the triple integral of f(x. y, ) - y over the region Use symbolic notation and fractions where needed.) +y S 3, x y, zso ydI help (fractions)
15.4 Integration in polar cylindrical spherical coordinates: Problem7 Previous Problem Problem List Next Problern (1 point Use sphenical coordinates to calculate the triple integral of...
3. (2 Points) Let Q be the quadrilateral in the ry-plane with vertices (1, 0), (4,0), (0, 1), (0,4). Consider 1 dA I+y Deda (a) Evaluate the integral using the normal ry-coordinates. (b) Consider the change of coordinates r = u-uv and y= uv. What is the image of Q under this change of coordinates?bi (c) Calculate the integral using the change of coordinates from the previous part. Change of Variables When working integrals, it is wise to choose a...
2. (18 pts) Consider an isosceles triangle that has its base on the x-axis. The apex of the triangle is at the point (O.y), where y > 0, and the remaining two vertices are at the points (x, 0) and (-x,0), where x > 0 (see figure). The area of the triangle is 120 in? This triangle lies inside a bigger isosceles triangle that also has its base on the x-axis. The apex of the bigger triangle is at the...