The finite element method (FEM) is one of the methods most used by engineers. It is a necessity for every engineer to understand this method. FEM is now an integral part of most structural analyses. In fact, we not only use FEM in daily analysis, but we also use FEM to optimize our structural designs. FEM tools allow us to quickly test many design variations. And it also optimizes our design. What I mean by optimization is a mass reduction of our structures. Nowadays, mass savings in our facilities leads to lower product costs, lower transportation costs and so on. FEM is very important for a structural engineer. It saves time, allows for rapid variation of designs, and is often used to bring out a lean product. We will mathematically analyze the FEM and then implement it in Java with the aim of plotting the temperature distribution in the profiles. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essayCalculate and plot the temperature distribution in the studied domain. For the 3 cases we plot the temperature distribution. Due to the symmetry around the y-axis, we can only do the calculations for the left or right side, we chose the right side. Since the heat flow only goes in the x direction (on the symmetry axis), we only have to do the calculations for the top. The heat flow goes from right to left (the heat flow vector is proportional to the negative temperature gradient). Knowing that the flow is perpendicular to the isotherms, the following results are physically logical. From the temperature distribution graph, we cannot conclude which profile has the highest thermal resistance. This is because thermal resistance is a global parameter and this temperature distribution is local. Calculate the thermal resistivity of the hollow wall for different configurations The goal of the profile is to insulate. The profile with the highest thermal resistance is by definition the best insulator. The best profile of the 3 cases is case C with a thermal resistance equal to R=2677 K/W. But the mechanical resistance of the profile must also be taken into account. The profile with the most air space is the best insulator (air is an excellent insulator compared to the profile material) but also the most fragile. So we need to find a balance between insulation properties and mechanical strength properties. To find the best profile we can vary the dimensions a, b, and store each value for the thermal resistance in an array. After the calculation, we look for the highest thermal resistance value in this optimally sized array. Perform a convergence study based on finite element mesh density and time calculation. We check the convergence with the resistance value: if the resistance does not change much if we increase the dichotomy, we can conclude that we have achieved convergence. We cannot achieve convergence due to “OutOfMemoryError”. The reason is that our code is not efficient with respect to memory usage. But from the figures we clearly see that the graphs reach a horizontal asymptote. This value of this horizontal asymptote is the convergent value of the thermal resistance. Draw the temperature profile inside the hollow wall between two points (e.g. between both sides). This figure represents the temperature profile with y=1 fixed for case c. The x coordinate goes from 0 to 10. Since the L profile is symmetrical, the temperature from x=-10 to x=0 will also be symmetrical. Now we are interested in an electrokinetic problem. The problem studied is a.