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

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