Finite elements are an invaluable technique for solving financial engineering problems that are presented as partial differential equations. This is a highly specialized topic with a vast literature crossing multiple disciplines. What Topper has done is compile a detailed survey of methodologies that are useful in finance. This is not really a financial engineering book. The author is clearly knowledgeable about the literature and recent developments in the financial engineering. He draws plenty of examples from the financial engineering literature, but this is really a book on finite elements written for financial engineers. Numerous techniques are discussed, and those discussions often open by presenting just a partial differential equation without any financial context. This isn't a criticism. It is just a warning that this really is a book on finite element (and to some extent finite difference) methods. It is somewhat of a book of recipes with citations to the liteature for addiitional information.

There are plenty of examples with detailed numerical output that readers can try to reproduce. It is a very technical book. You want to have prior familiarity with financial engineering and partial differential equations. Some familiarity with finite difference and finite element methods would also be helpful, but it isn't necessary.