Implement the weak form in comsol

Assignment Help Mechanical Engineering
Reference no: EM13859602

Objectives-

• To understand the general procedure of finite element formulation.

• To appreciate convergence and learn error estimation.

A) The 2n° order ODE

(d2u/dx2) + sinx = 0

with boundary conditions u(0) = 0 and u'(2Π) =1 has analytical solution

u(x) = sin x

The Galerkin weak form of this ODE is

0[- (du/dx)(dδu/dx) + sin x δu(x)] dx δu(2Π) = 0,      ∀Su(x)

with essential boundary condition u(0) = 0.

1) Implement the weak form in COMSOL, and experiment on the effect of element size and type. You may control the mesh by selecting "User-controlled mesh" under meshing and specific the maximum element size. For element type, you may open "Discretization" under "Weak form PDC' (if not shown, toggle on the option by clicking on the "eye" icon on top-left of the "Model builder").

Test Lagrange elements of all possible orders.

2) Calculate the L2 error of all cases of your study

||e||L2 = [∫7 (Uapprox -uexact)2dx]1/2

and plot the error of each element type (order) in one curve as a function of the element size.
Use log-log plot to show the general trend. You may evaluate the integral by right click on "ResultskDerived ValuesilntegrationiLine Integration", select the line, and type in the expression (integrand).

3) Re-plot the L2 error against the total number of nodes in each case (copy the results out and plot it in other software, say excel). Which element is more efficient?

4) Plot the distribution of the error of the derivative, e(x) = (du/dx) - cos x, for linear and quadratic elements (by meshing the interval into 1 or 2 element). Where are the results of derivatives more accurate?

B) Now consider the ODE

(d2u/dx2) + (1/4)x3/2= 0

with essential boundary conditions u(0) = 0 and u(1) = 1. Repeat steps (1)-(3) of the last problem for this equation. The exact solution for this equation is

u(x) = x1/2

Reference no: EM13859602

Questions Cloud

Summary or review about this film - kelly loves tony : Watch the Film/video: Kelly Loves Tony. and write an outline. I don't have the resource for this film, you can search the summary or review about this film to do this assignment
Values of the price level : Assume that the long-run aggregate supply curve is vertical at Y = 3,000 while the short-run aggregate supply curve is horizontal at P = 1.0. The aggregate demand curve is Y = 2(M/P) and M = 1,500. If the economy is initially in long-run equilibri..
Discuss the benefits to ups of the corporate sustainability : Discuss the benefits to UPS of the corporate sustainability report
Banning imports of low-wage asian clothing : 1. A representative of the American clothing industry recently made the following statement: "Workers in Asia often work in sweatshop conditions earning only pennies an hour. American workers are more productive and as a result earn higher wages. ..
Implement the weak form in comsol : Implement the weak form in COMSOL, and experiment on the effect of element size and type. You may control the mesh by selecting "User-controlled mesh" under meshing and specific the maximum element size.
Explain the need for full disclosure in financial reporting : Explain the need for full disclosure in financial reporting
Understanding the furiously religious world that we live in : Use our course texts on the Christian, Buddhist, and Islamic traditions to try to convince Dr. Stephen Prothero that his multiple mountain metaphor for studying religious traditions is not a perfect solution to understanding the "furiously religio..
Identify the stressors in john breckenridges life : Identify the stressors in John Breckenridge's life. Which ones could he have prevented?
How is pricing determined in the fulfillment process : How is pricing determined in the fulfillment process? Provide examples of data relevant to pricing.

Reviews

Write a Review

Mechanical Engineering Questions & Answers

  Package design

Package Design Brief: Assume you are the packaging engineer for a large consumer products company. In this company, the Packaging Design Briefs are initiated by the marketing group and forwarded to the Package Engineering group.

  Mechanical engineering questions

Define dynamic viscosity, Determine the centroid, Pressure due to the height of liquid, Advantage of changing the liquid, Calculate the total moment about the hinge of the seal gate.

  Automatic control

DOF system and Find the differential equation describing the system

  Write a paper on boyle''s law

Write a paper on Boyle's law and describe Compression and Combustion stroke . Also explain Charles's law and illustrate SI engine and CI engine.

  Verify the law for parallelogram of forces

To Verify the law for parallelogram of forces, law for triangle of forces and law of polygon of forces. These laws are very useful to calculate unknown forces in very short time.

  Discharge pressure of the compressor

What is the discharge revised discharge pressure of the compressor.

  The Case for Global Accounting Standards

The role of IFRS in both developing and developed capital markets.

  Wind turbine

Wind turbines are becoming more and more common as a method of energy production, wind turbines by their very nature are dynamic and are subject to and create their own internal and external kinematics and kinetics.

  Advanced design methodologies

8 x product engineering and design review (week 2 – 12), ~3 pages per item which must contain a brief description of the product then delve into concepts such as materials selection, manufacturing methods, life cycle analysis, recyclability and overa..

  Design of absorption column and the cooler

Design of absorption column and the cooler. Process design of other units should be completed along with pipe sizes.

  Determine the maximum total bending moment

Determine maximum total bending moment (static plus dynamic) of the beam under steady-state conditions.

  Force of the water on the gate

Determine the magnitude of the horizontal and vertical components of the force of the water on the gate.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd