$$ \newcommand{\tp}{\thinspace .} \newcommand{\x}{\boldsymbol{x}} \renewcommand{\u}{\boldsymbol{u}} \renewcommand{\v}{\boldsymbol{v}} \newcommand{\V}{\boldsymbol{V}} \newcommand{\baspsi}{\psi} \newcommand{\dx}{\, \mathrm{d}x} $$

Variational forms for systems of PDEs

Hans Petter Langtangen [1, 2]

[1] Center for Biomedical Computing, Simula Research Laboratory
[2] Department of Informatics, University of Oslo

Oct 16, 2015


PRELIMINARY VERSION

Table of contents

Variational forms
      Sequence of scalar PDEs formulation
      Vector PDE formulation
A worked example
Identical function spaces for the unknowns
      Variational form of each individual PDE
      Compound scalar variational form
      Decoupled linear systems
      Coupled linear systems
Different function spaces for the unknowns
Computations in 1D
Bibliography