### The Dutch House

I don’t understand how a book like The Dutch House can be so captivating. There are no overarching villain, nor fantastical world building or gimmicks. The sole driving force lies in the ability of Ann Patchett to deliver a soulful story stemming from the Cinderella-esque expulsion of two siblings, Maeve and Danny, from their family “home,” the Dutch House.

The two trudged into the future, with Danny obtaining a medical degree but ultimately eschewing it by becoming a real estate investor while Maeve became a successful CFO figure in a frozen vegetable company, while never letting go of the past, returning to the edges of the Dutch House time after time; partly out of habit, and partly to reminisce. It was in those quiet times where the author really shined and captured my attention, and drove me to keep on reading. Turns out, I have been and will always be a sucker for good prose.

I know I am facing a lot of personal issues  this quarantine, and the following quote resonated:

There are a few times in life when you leap up and the past that you’d been standing on falls away behind you, and the future you mean to land on is not yet in place, and for a moment you’re suspended, knowing nothing and no one, not even yourself.

I am at a crossroads in my life with finishing up my degree. I’ve just been through a tough breakup. I will land on solid ground though. I need to focus on not what I have lost, but rather what I can achieve:

I’d never been in the position of getting my head around what I’d been given. I only understood what I’d lost.

### Sixty Days Later

The year started off like any other year, with the exception that there were significantly more ophthalmology based puns, until a little virus blossomed into a pandemic. The resulting quarantine is messy: toilet paper became a commodity worth it’s volume in gold, Zoom overtook Skype as the de facto way to FaceTime people, and the Baskin-Robbins logo is associated with Joe Exotic.

Another tragedy is my haircut. I’ve never really liked how my coiffure looked after an appointment, and I always say “it’ll look better after a few days.” This was a lie. The truth is, my hair didn’t get better. It was moreso I settled. It was (and still is) basically an unhappy relationship.

The barber always asked me how I wanted it cut, and I always replied “It was four weeks ago since my last haircut” then they trim off four weeks worth of hair and happily take my twenty dollars plus tip. The problem is, I usually never liked what my hair looked like four weeks ago, nor that haircut from eight weeks ago ad infinitum. Just a reminder, my hair looked like:

Within the last few months, I actually became more comfortable with my hair. And now, with this stupid quarantine, I’m going to stroll into the barbershop looking like the Geico caveman

### A note on a paper by Babuska

This is a post regarding the paper Efficient Preconditioning for the $p$-Version Finite Element Method in Two Dimensions. In Lemma 3.3, the basis required is the bubble (or interior) polynomials, the set of edge functions orthogonal to the interiors, and linear (of bilinear) functions.

The edge functions orthogonality is explicitly stated as $\hat a(u, v) = 0$ for all $u \in \Gamma_i$ (edge space) and $v \in \mathcal{I}$ interior space. A very natural question is why the vertex functions does not need to be orthogonal to the interior functions. The fun fact is that it secretly is.

Note that the paper is for the $H^1$ semi-norm, hence $\hat a(u, v) = \int_T \nabla u \nabla v \, dx$. Now let $u$ be a hat (or bilinear) function, and let $v \in \mathcal{I}$. Then we have that
\begin{align*}
\int_T \nabla u \nabla v = \int_{\partial T} u \partial_n v – \int_T \Delta u v = 0.
\end{align*}
The first term is 0 due to the bubble functions vanishing on the boundary, and that $\Delta u = 0$ because it is linear.