Mixing
Finite-difference vs finite-volume schemes for conservation laws
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As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
Why is this so?
What is the difference between solutions of transport equation and conservation laws when flux is not linear?
What happens if we use finite volume schemes for transport equation?
pde numerical-methods hyperbolic-equations transport-equation
edited Jan 10 at 9:07
Harry49
6,18331132
asked Jan 9 at 17:20
RosyRosy
1095
$endgroup$
add a comment |
$begingroup$
As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
Why is this so?
What is the difference between solutions of transport equation and conservation laws when flux is not linear?
What happens if we use finite volume schemes for transport equation?
pde numerical-methods hyperbolic-equations transport-equation
edited Jan 10 at 9:07
Harry49
6,18331132
asked Jan 9 at 17:20
RosyRosy
1095
$endgroup$
add a comment |
$begingroup$
As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
Why is this so?
What is the difference between solutions of transport equation and conservation laws when flux is not linear?
What happens if we use finite volume schemes for transport equation?
pde numerical-methods hyperbolic-equations transport-equation
edited Jan 10 at 9:07
Harry49
6,18331132
asked Jan 9 at 17:20
RosyRosy
1095
$endgroup$
As far as I know we don't use finite difference scheme for conservation law because solution of conservation law makes no sense pointwise as its only in $L^{infty}$. But however we use finite difference scheme for linear transport equation ($u_t+au_x=0$), which is a conservation law with flux $f(u)=au$.
Why is this so?
What is the difference between solutions of transport equation and conservation laws when flux is not linear?
What happens if we use finite volume schemes for transport equation?
pde numerical-methods hyperbolic-equations transport-equation
pde numerical-methods hyperbolic-equations transport-equation
edited Jan 10 at 9:07
Harry49
6,18331132
asked Jan 9 at 17:20
RosyRosy
1095
edited Jan 10 at 9:07
Harry49
6,18331132
asked Jan 9 at 17:20
RosyRosy
1095
edited Jan 10 at 9:07
Harry49
6,18331132
edited Jan 10 at 9:07
Harry49
6,18331132
edited Jan 10 at 9:07
Harry49
6,18331132
6,18331132
asked Jan 9 at 17:20
RosyRosy
1095
asked Jan 9 at 17:20
RosyRosy
1095
asked Jan 9 at 17:20
RosyRosy
1095
1095
add a comment |
add a comment |
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