An introduction to the finite element method for differential equations

Book, 2020

This text introduces the Galerkin finite element method for approximate solution of differential equations. It starts with a modern theoretical approach to the well-posedness issue, physical derivations of the equation as well as mathematical tools. Both initial- and boundary value problems are treated in single- and multi-dimensions and stability, and convergence are discussed and proved in details. The converhence analysis are in "a priori" (theoretical) as well as "a posteriori" (computational) settings. There are MATLAB-codes to test different application examples. The text is designed to be accessible for upper-level undergraduates and graduate students in applied science and engineeering disciplines.