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Finite Element Method

Finite element method is a numerical technique for finding approximate solutions to boundary value problems. It uses variation methods to minimize an error function and produce a stale solution. Finite element method encompasses all the methods for connecting many simple element equations over many small subdomains, named finite elements, to approximate a more complex equation over a larger domain.

A typical work out of the method involves dividing the domain of the problem into a collection of subdomains, with each subdomain represented by a set of element equations to the original problem, followed by systematically recombining all sets of element equations into a global system of equations for the final calculation.

The element equations are simple equations that locally approximate the original complex equations to be studied, where the original equations are often partial differential equations. The finite element method is commonly introduced as a special case of Galerkin method. The process is to construct an integral of the inner product of the residual and the weight functions and set the integral to zero.

Finite element methods are a good choice for analyzing problems over complicated domains, when the domain changes, when the desired precision varies over the entire domain, or when the solution lacks smoothness. An example of this would be in numerical weather prediction where it is more important to have accurate predictions over developing highly nonlinear phenomena rather than relatively calm areas. 

Matrix and Linear Equations

Please provide assistance in understanding how to prove whether or not finite mathematical equations are true or false. I have attached the questions that I am experiencing difficulty on. In your solution, please explain how to prove, i.e., your recommendation on the specific formula I should use. My textbook does not provide th

Continuous Method for Time Recording

See the attached file. When performing time study process insurance claims adjusting company doctors Triple R, Barney Rubble analyst applies the continuous method for time recording. The activity is divided into four work items. In Figure 7.3 (attached) are the rating factors (RF) performance and the times recorded by the con

Mathematics - Modified Distribution Method

Solve the problem using Modified Distribution Method 1. The ABC Umbrella Factory has received a letter from a regular customer ordering umbrellas for his 3 department stores: Store Monthly Requirement Plaza Fair 250 Fair Mart

Elements in an Abelian Group

Let G be the direct sum of a countably infinite number of copies of Z. Find an element of End_Z(G) which has a left inverse, but is not a unit. Please explain in detail. Think of elements of End_Z(G) as infinite matrices with integer entries. Definition: Let G be an abelian group and let End_Z(G) be the set of all grou

Mathematical Method for Economics

1. The per period sales of a new product, x(t), evolves over time according to x(t):= A / (1 + b * e - c t ) where A, b and c are positive constants. a) By taking the limit of x(t) as t tends to infinity, show that per period sales tends to A as t increases. b) Show that the rate of growth of sales is proportional to

Prove that every element of a susbet is of finite order.

Let G= , x*y be the fractional part of x+y .(i.e:x*y=x+y-[x+y] where [a] is the greatest integer less than or equal than a). Show that all the elements of the subset of all rational elements of this group are of finite order. Please see the attached file for the fully formatted problems.

Newton's Method and Four Rectangles and the Right Endpoint Method

Question #1. Find the positive root of the equation cos(x) = sin(x) + x^4 using Newton's method (Do only 3 iterations). Question #2. The acceleration of object is given by the following equation: a(t) = cost(t) - 3t^2 + e^t. We also know that v(0) = 8cm/sec and s(0) = 32cm. Find the position of the object after 3 seconds.

Finite Difference Methods for PDEs

B. A beam is resting horizontally on the sharp edges of a room with width L, and has a ceiling attached in the shape .... At time t = 0 the glue releases and the beam vibrates. Describe the vibration for t > 0 if the situation is described by ... Boundary and initial values are given by ..... Hint: Use separation of variab

Basis and Finite and Infinite Field Extensions

Find a basis for the extension of and also calculate We know already that is infinite. Give an example of fields and (with neither nor equal to ) such that: a) and are both infinite b) is infinite and is finite. (See attached file for full problem description with proper symbols) All gaps are Q,

Newton's method

Use Newton's method to approximate the x value of the point near x=3 of 2 functions 1. f(x) = 3 - x 2. g(x) = 1/(x^2) + 1 Do this problem for complete iterations to get an answer of about .001 of the real value hint let H(x) = f(x) - g(x)

Conjugacy Classes of A Finite Group Problem

G is a finite group with elements a and b. Let the conjugacy classes of these elements be A and B respectively and suppose |A|^2, |B|^2 < |G|. Prove that there is a non-identity element x in G s.t. x commutes with both a and b.


Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity A) S = Q X p Y <-> ABS(X) <= ABS(Y) B) S = Z X p Y <-> x -y is an integral multiple of 3 C) S = N X P Y <-> X is odd D) S = Set of all squares in the place S1 p S2 <-> length of side of S1 = length of side S2 E)

It is dealing with finite automatons

(a)For each of the following languages over the unary alphabet {a}, construct a finite automaton accepting it. i. {a^2} ii. {a^2, a^3, a^4} (b) Let A be any finite nonempty subset of {a, a^2, a^3, a^4,...}. Is there always a finite automaton that accepts A?

Golden Search method

My professor gave us a golden search problem to practice on, and he gave us the answer. I can not get to the same place he did. I think I am not selecting the intervals of uncertainty correctly, but I am not sure. Can you help? The attached file has the problem, and the way I worked it.