Optimal error estimates in <mml:math alttext="$L^2 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>L</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>, <mml:math alttext="$H^1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math> and <mml:math alttext="$H^2 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>H</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by an <mml:math alttext="$H^1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>-Galerkin procedure.

An <mml:math alttext="$H^1 $" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>H</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

An <svg style="vertical-align:-0.0pt" height="15.8375" version="1.1" viewBox="0 0 21.362499 15.8375" width="21.362499" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,15.775)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28&#xA;h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g><g transform="matrix(.012,-0,0,-.012,14.975,7.613)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g></svg>-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

International Journal of Mathematics and Mathematical Sciences

Abstract

Copyright

An H1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

https://www.hindawi.com/journals/ijmms/1987/797621/